In this paper, we classify parabolic revolution surfaces in the three-dimensional simply isotropic space 𝕀3 under the condition ΔJxi=λixi,J=I,II, where ΔJ is the Laplace operator with respect to first and second fundamental form and λi, i=1,2,3 are some real numbers. Also, as an application, we give some explicit examples for these surfaces.

We consider a timelike sweeping surface with rotation minimizing frames in Minkowski 3-Space 𝔼13. We introduce a new geometric “invariant”, which demonstrates the geometric properties and local singularities of the surface. Subsequently, we give the sufficient and necessary conditions for this surface to be a developable ruled surface. Finally, the singularities of these ruled surfaces are investigated

In this paper, we study the geometry of a certain class of compact dynamical horizons with a time-dependent induced metric in locally rotationally symmetric class II spacetimes. We first obtain a compactness condition for embedded 3-manifolds in these spacetimes, satisfying the weak energy condition, with non-negative isotropic pressure p. General conditions for a 3-manifold to be a dynamical horizon

We show that the scalar curvature of a K-contact Ricci soliton is constant and satisfies sharp bounds. Next we show that the scalar curvature of a (2n+1)-dimensional K-contact Ricci almost soliton is equal to 2n(2n+1) plus the divergence of a global vector field. Finally, we show that, if a complete connected Sasakian or η-Einstein K-contact manifold of dimension >3 is a proper Ricci almost soliton

In this paper, DeWitt’s formalism for field theories is presented; it provides a framework in which the quantization of fields possessing infinite-dimensional invariance groups may be carried out in a manifestly covariant (non-Hamiltonian) fashion, even in curved space-time. Another important virtue of DeWitt’s approach is that it emphasizes the common features of apparently very different theories

We show that our Universe lives in a topological and non-perturbative vacuum state full of a large amount of hidden quantum hairs, the hairons. We will discuss and elaborate on theoretical evidences that the quantum hairs are related to the gravitational topological winding number in vacuo. Thus, hairons are originated from topological degrees of freedom, holographically stored in the de Sitter area

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces provided that Hamilton–Jacobi equation and Klein–Gordon–Fock equation for a charged test particle can be integrated by the method of complete separation of variables are found. The separation is carried out using the complete sets of mutually commuting integrals of motion of type (1.1) whereby in a privileged

This paper investigates stability of thin-shell developed from the matching of interior traversable wormhole with exterior Ayon–Beato–Garcia–de Sitter regular black hole through cut and paste approach. We employ Israel formalism and Lanczos equations to obtain the components of surface stress-energy tensor at thin-shell. These surface stresses violate null and weak energy conditions that suggest the

In this paper, we use the generalized Dirac structure beyond the linear regime of graphene. This is probed using the a deformation of the Dirac structure in graphene by the generalized uncertainty principle. Here, the Planck length is replaced by the graphene lattice spacing. As the graphene sheet is bounded by two boundaries, we analyze this system with suitable boundary conditions. We solve the perturbed

In the present work, we construct the Tsallis holographic quintessence model of dark energy in f(R,T) gravity with Hubble horizon as infrared (IR) cut-off. In a flat Friedmann–Robertson–Walker (FRW) background, the correspondence among the energy density of the quintessence model with the Tsallis holographic density permits the reconstruction of the dynamics and the potentials for the quintessence

We are interested in defining new energy functionals and solving them by using the variational approach method and Darboux equations. That is, we aim to define a new class of elastic curves on the regular surface Λ. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves on Λ. As a result, we classify these critical curves

Using the loop quantum gravity, based on polymer quantization, we will argue that the polymer length (like string length) can be several orders larger than the Planck length, and this can have low energy consequences. We will demonstrate that a short distance modification of a quantum system by polymer quantization and by string theoretical considerations can produce similar behavior. Moreover, it

In this paper, we introduced and established some group invariant results of (2+1)-dimensional mKdV–Calogero–Bogoyavlenskii–Schiff equation. Using the one-parameter Lie-group of transformations, we explored various closed-form solutions. The procedure minimizes the number of independent variables by one in every proceeding stage leading to form a system of the ordinary differential equations. The nature

In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of an orthogonal matrix in 3-dimensional generalized space E3(α,β). It is shown that unit generalized quaternion, which is defined by the generalized Euler parameters, corresponds to a rotation in E3(α,β) space.We found that the rotation in matrix equation forms using matrix form of the generalized quaternion

In this paper, the multifluid equations of a plasma are reformulated in terms of conic sedenions in order to better reflect the analogies between multifluid plasma equations and Maxwell equations of classical electromagnetism. This formalism also provides us an efficient mathematical tool for unification of equations of fluid dynamics and electromagnetism in a compact and elegant way. Although the

In this work, the cosmological inflationary parameters in the correspondence of teleparallel gravity for the scalar–tensor theory are investigated. After the review of f(T) and f(T,B) gravity cosmology, we use the slow-roll approximations to study the behavior of the inflationary parameters namely the spectral index ns and tensor-to-scalar ratio r, and a comparison with observational data for different

In this paper, we investigate a scalar field Brans–Dicke cosmological model in Lyra’s geometry which is based on the modifications in a geometrical term as well as energy term of Einstein’s field equations. We have examined the validity of the proposed cosmological model on the observational scale by performing statistical analysis from the latest H(z) and SN Ia observational data. We find that the

Several methods use the Fourier transform from momentum space to twistor space to analyze scattering amplitudes in Yang–Mills theory. However, the transform has not been defined as a concrete complex integral when the twistor space is a three-dimensional complex projective space. To the best of our knowledge, this is the first study to define it as well as its inverse in terms of a concrete complex

We discuss the generalization of phenomenological equations for electromagnetic field in superconductor based on algebra of space-time sedeons. It is shown that the combined system of London and Maxwell equations can be reformulated as a single sedeonic wave equation for the field with nonzero mass of quantum, in which additional conditions are imposed on the scalar and vector potentials, relating

With due consideration of reasonable cosmological assumptions within the limit of the present cosmological scenario, we have analyzed a spherically symmetric metric in 5D setting within the framework of Lyra manifold. The model universe is predicted to be a DE model, dominated by vacuum energy. The model represents an oscillating model, each cycle evolving with a big bang and ending at a big crunch

The evolute of a regular curve in the Lorentz–Minkowski plane is given by the locus of centers of osculating pseudo-circle of the base curve. But the case when a curve has singularities is not very clear. In this paper, we use lightcone frame to define the (n,m)-cusp mixed-type curves and their evolutes in Lorentz–Minkowski plane. In order to attain this goal, we define the (n,m)-cusp non-lightlike

In this work, we explore the accelerated expansion of the conharmonically flat space in relation to an isotropic and spatially homogeneous Friedmann–Robertson–Walker (FRW) universe through a newly proposed dark energy (DE) model namely Sharma–Mittal holographic DE (SMHDE) by taking Hubble horizon as an IR cut-off and also by considering the deceleration parameter as a linear function of Hubble parameter

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss–Bonnet theorem to the optical geometry of asymptotically flat black holes and apply the Gibbons–Werner technique to achieve the deflection angle of photons in weak field limits

The characterization of curves plays an important role in both geometry and topology of almost contact manifolds. Olszak found the equation 2αβ+ξ[β]=0 on normal almost contact manifolds. The pair (α,β) denotes the type of these manifolds. In this study, we obtained the curvatures of non-geodesic Frenet curves on 3-dimensional normal almost contact manifolds without neglecting α and β, and provided

We analyze the existence of equilibrium points for a particle or dust grain in the framework of unperturbed and perturbed Robe’s motion. This particle is moving in a spherical nebula consisting of a homogeneous incompressible fluid, which is considered as the primary body. The second primary body creates the modified Newtonian potential. The perturbed mean motion and equations of motion are found.

The purpose of the offering exposition is to characterize gradient Yamabe, gradient Einstein and gradient m-quasi Einstein solitons within the framework of 3-dimensional para-Kenmotsu manifolds. Finally, we consider an example to prove the result obtained in previous section.

For the spherical unit speed nonlightlike curve in pseudo-hyperbolic space and de Sitter space γ and a given point P, we can define naturally the pedal curve of γ relative to the pedal point P. When the pseudo-sphere dual curve germs are nonsingular, singularity types of such pedal curves depend only on locations of pedal points. In this paper, we give a complete list of normal forms for singularities

In this work, we compute the time evolution equations (TEEs) of the type-1 Bishop frame of the curve. Also, we study the time evolution equations for type-1 Bishop curvatures (TEEBCs) as a system of partial differential equations (PDEs). Through this study, we give a necessary and sufficient condition for the normal and binormal Bishop velocities. Also, we construct new models of normal motions of

In the frame work of Saturn–Titan system, the resonant orbits of first-order are analyzed for three different families of periodic orbits, namely, interior resonant orbits, exterior resonant orbits and f-Family orbits. This analysis is developed by considering Saturn as a spherical and oblate body. The initial position, semi-major axis, eccentricity, orbital period and order of resonant orbits of these

This paper is fundamentally devoted to the cosmological reconstruction and dynamic studying in homogeneous BIANCHI-I space-time under the f(T) background. Its content is supported by the fact that in the General Relativity description of the standard cosmological paradigm, the evolution from an anisotropic universe into an Friedmann–Lemaitre–Robertson–Walker (FLRW) one can be achieved by a period of

We deal with non-autonomous Hamiltonian systems of one degree of freedom. For such differential systems, we compute analytically some of their periodic solutions, together with their type of stability. The tool for proving these results is the averaging theory of dynamical systems. We present some applications of these results.

In this work, we propose a non-interacting model of Barrow holographic dark energy (BHDE) using Barrow entropy in a spatially flat FLRW Universe considering the IR cutoff as the Hubble horizon. We study the evolutionary history of important cosmological parameters, in particular, deceleration parameter, equation of state (EoS) parameter, the BHDE and matter density parameter, and also observe satisfactory

Developable surfaces are defined to be locally isometric to a plane. These surfaces can be formed by bending thin flat sheets of material, which makes them an active research topic in computer graphics, computer aided design, computational origami and manufacturing architecture. We obtain condition for developable and minimal ruled surfaces using rotation frame. Also, the validity of the theorems is

Although it is not a fundamental question, determining exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski–Sachs spacetime describes a homogeneous but anisotropic universe whose spatial section

The aim of this paper is to investigate Killing magnetic trajectories of varying electrically charged particles in a three-dimensional warped product I×f𝔼2 with positive warping function f, where I is an open interval in ℝ equipped with an induced semi-Euclidean metric on ℝ. First, Killing vector fields on I×f𝔼2 are characterized and it is observed that lifts to I×f𝔼2 of Killing vector fields tangent

In this paper, we analyze the thermodynamic stability of Schwarzschild Modified Gravity (MOG) black holes in a non-commutative framework. We show that, unlike a commutative MOG black hole, in the coherent state picture of non-commutativity MOG black holes are thermodynamically stable. At the final stage of evaporation a stable remnant with zero temperatures and finite entropy is left in this non-commutative

Collapsing process is studied in special type of inhomogeneous spherically symmetric space-time model (known as IFRW model), having no time-like Killing vector field. The matter field for collapse dynamics is considered to be perfect fluid with anisotropic pressure. The main issue of this investigation is to examine whether the end state of the collapse to be a naked singularity or a black hole. Finally

We construct the thermodynamic geometry of (2+1)-dimensional normal (exotic) BTZ black hole regarding the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat space, the three-dimensional space of thermodynamics parameters including the cosmological constant as a fluctuating parameter

In this study, we provide a brief description of rotational surfaces in 4-dimensional (4D) Galilean space using a curve and matrices in G4. That is, we provide different types of rotational matrices, which are the subgroups of M by rotating a selected axis in E4. Hence, we choose two parameter matrices groups of rotations and we give the matrices of rotation corresponding to the appropriate subgroup

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in

In this paper, we investigate the effects of Type IV singularity through f(T) gravity description of inflationary Universe, where T denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a f(T) model according to a given Hubble rate susceptible to describe the inflationary era near the Type IV singularity. One obtains an interesting well-known f(T) model but with additional

In this paper, Jacobi stability of a segmented disc dynamo system is geometrically investigated from viewpoint of Kosambi–Cartan–Chern (KCC) theory in Finsler geometry. First, the geometric objects associated to the reformulated system are explicitly obtained. Second, the Jacobi stability of equilibria and a periodic orbit are discussed in the light of deviation curvature tensor. It is shown that all

In this work, we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially, we present a general formulation through elements of minimal left ideals in tensor products of Clifford algebras. Posteriorly, we perform some applications in quantum computation: qubits, entangled states, quantum gates, representations of the braid

We test whether static charged dilaton black holes in (2+1) dimensions can be turned into naked singularities by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also implies that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal

In this paper, first, we will try to introduce the gravitational domain wall as a physical system. In the second step, we also introduce the Hun differential equation as a mathematical tools. We factorize the known Heun’s equation as form of operators P+, P− and P0. Then we compare the differential equation of gravitational domain wall with corresponding Hun equation. In that case the above-mentioned

The main aim of this work is to build unitary phase operators and the corresponding temporally stable phase states for the su(n+1) Lie algebra. We first introduce an irreducible finite-dimensional Hilbertian representation of the su(n+1) Lie algebra which is suitable for our purpose. The phase operators obtained from the su(n+1) generators are defined and the phase states are derived as eigenstates

The aim of this paper is to establish a generalization of the Born geometry to ρ-commutative algebras. We introduce the notion of Born ρ-commutative algebras and study the existence and uniqueness of a torsion connection which preserves the Born structure. Also, an analogue of the fundamental theorem of Riemannian geometry will be proved for these algebras.

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

Stability, dark energy (DE) parameterization and swampland aspects for the Bianchi form-VIh universe have been formulated in an extended gravity hypothesis. Here, we have assumed a minimally coupled geometry field with a rescaled function of f(R,T) replaced in the geometric action by the Ricci scalar R. Exact solutions are sought under certain basic conditions for the related field equations. For the

Our aim is to discuss spherically symmetric static wormholes with the Lorentzian signature in the Einsteinian cubic gravity for two different models of pressure sources. First, we calculate the modified fields equations for the Einsteinian cubic gravity for the wormhole geometry under the anisotropic matter. Then we investigate the shape-function for two different models, which can be taken as a part

The Noether–Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the Noether–Bessel-Hagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select

This paper is devoted to formulate a new model of quintessence anisotropic compact stars in the modified f(R,G) gravity. Dynamical equations in modified theory consisting of anisotropic fluid along with quintessence field have been evaluated by adopting analytical solution of Krori–Barua. In order to determine the unknown constraints of Krori–Barua metric observational data of different stars, 4U1820-30

The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic

The aim of this paper is to classify non-conformally flat static plane symmetric (SPS) perfect fluid solutions via proper conformal vector fields (CVFs) in f(T) gravity. For this purpose, first we explore some SPS perfect fluid solutions of the Einstein field equations (EFEs) in f(T) gravity. Second, we utilize these solutions to find proper CVFs. In this study, we found 16 cases. A detailed study

We define a functional 𝒥(h) for the space of Hermitian metrics on an arbitrary Higgs bundle over a compact Kähler manifold, as a natural generalization of the mean curvature energy functional of Kobayashi for holomorphic vector bundles, and study some of its basic properties. We show that 𝒥(h) is bounded from below by a nonnegative constant depending on invariants of the Higgs bundle and the Kähler

We study solitons of almost pseudo symmetric Kählerian space-time manifold. It is considered that different curvature tensors like projective, conharmonic and conformal curvature tensors in almost pseudo symmetric Kählerian space-time manifolds are flat. It is shown that solitons are steady, expanding or shrinking under different relations of isotropic pressure, the cosmological constant, energy density

A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational interaction, and a key to quantum gravity. Inspired by Souriau’s symplectic generalization of the Maxwell–Boltzmann–Gibbs equilibrium in Lie group thermodynamics, we investigate

We analyze the parity violation issue in the Poincaré gauge theory of gravity for the two classes of models which are built as natural extensions of the Einstein–Cartan theory. The conservation laws of the matter currents are revisited and we clarify the derivation of the effective Einstein field equation and the structure of the effective energy–momentum current for arbitrary matter sources.

We propose a new unified model that describes dark energy and dark matter in the context of f(R,ϕ) gravity using a massive scalar field in five dimensions. The scalar field is considered in the bulk that surrounds the 3-brane in branworld model. We show that for a specific choice of the f(R,ϕ) function, we can describe the Einstein gravitation in 4-dimensional space-time. We obtain a relationship between

In this paper, we investigate the charged static spherically symmetric models in f(R) theory of gravity. We consider a linear equation of state (EoS) in the background of anisotropic matter configuration. We formulate the modified field equations and implement Durgapal transformation to examine the gravitational nature of compact stellar objects. For this purpose, we choose a specific gravitational