In this paper, a (2+1)-dimensional variable-coefficients Calogero–Bogoyavlenskii–Schiff (vcCBS) equation is studied. The infinitesimal generators and symmetry groups are obtained by using the Lie symmetry analysis on vcCBS. The optimal system of one-dimensional subalgebras of vcCBS is computed for determining the group-invariant solutions. On this basis, the vcCBS is reduced to two-dimensional partial

In this paper, we give a complete classification of Yamabe solitons and gradient Yamabe solitons on real hypersurfaces in the complex quadric Qm=SOm+2/SO2SOm. In the following, as an application, we show a complete classification of quasi-Yamabe and gradient quasi-Yamabe solitons on Hopf real hypersurfaces in the complex quadric Qm.

The main objective of this paper is to establish Heisenberg’s and Beckner’s uncertainty principles associated with multi-dimensional linear canonical transform.

In this paper, the propagation of cylindrical shock wave in rotating non-ideal gas under adiabatic flow condition using Lie group of transformation method is investigated. The density is assumed to be constant and azimuthal fluid velocity is assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the Local Lie group of transformations

In this paper, we study the biharmonic submanifolds of Riemannian manifolds endowed with metallic and complex metallic structures. In case of both the structures, we obtain the necessary and sufficient conditions for a submanifold to be biharmonic. Particularly, we find the estimates for mean curvature of Lagrangian and complex surfaces.

In this paper, we study the mechanism of the cosmic model in the presence of generalized ghost pilgrim dark energy (GGPDE) and matter in locally rotationally symmetric (LRS) Bianchi type-I space-time by the utilization of new holographic DE in Saez–Ballester theory. Here, we discuss all the data for three scenarios, the first is supernovae type-Ia union data, the second is SN Ia data in combination

The evolutes of regular curves in the Euclidean plane are given by the caustics of regular curves. In this paper, we define the generalized evolutes of planar curves which are spatial curves, and the projection of generalized evolutes along a fixed direction are the evolutes. We also prove that the generalized evolutes are the locus of centers of slant circles of the curvature of planar curves. Moreover

In this paper, first, we introduce the notion of a generalized Reynolds operator on a 3-Lie algebra 𝔤 with a representation on V. We show that a generalized Reynolds operator induces a 3-Lie algebra structure on V, which represents on 𝔤. By this fact, we define the cohomology of a generalized Reynolds operator and study infinitesimal deformations of a generalized Reynolds operator using the second

In this study, we survey the generalized Duffin–Kemmer–Petiau oscillator containing a non-minimal coupling interaction in the context of rainbow gravity in the presence of the cosmic topological defects in space-time. In this regard, we intend to investigate relativistic quantum dynamics of a spin-0 particle under the modification of the dispersion relation according to the Katanaev–Volovich geometric

In this short note, we will prove in a few steps that the new tetrads introduced previously in Einstein–Maxwell–Yang–Mills four-dimensional Lorentzian spacetimes where gravitational and Yang–Mills fields are present contain both the necessary information to provide the gravitational field and the necessary information to provide the electromagnetic and Yang–Mills fields as well. These new tools thus

We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations eσi in the spin representation (a.k.a. Lorentz rotors) in terms of their generators σi: ln(eσ1eσ2)=tanh−1tanhσ1+tanhσ2+12[tanhσ1,tanhσ2]1+12{tanhσ1,tanhσ2}. This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension ≤4, naturally generalizing Rodrigues’ formula

In this paper, we introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative-dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can derive naturally from the non-orientability

The geometric theory of additive separation of variables is applied to the search for multiplicative separated solutions of the bi-Helmholtz equation. It is shown that the equation does not admit regular separation in any coordinate system in any pseudo-Riemannian space. The equation is studied in the four coordinate systems in the Euclidean plane where the Helmholtz equation and hence the bi-Helmholtz

In an attempt to find the dynamical foundations for q-entropies, we examine the special case of Lagrangian/Hamiltonian systems of many degrees of freedom whose statistical behavior is conjecturally described by the q-entropic functionals. We follow the spirit of the canonical ensemble approach. We consider the system under study as embedded in a far larger total system. We explore some of the consequences

In this study, a pseudo-null space curve in Minkowski 3-space is used to describe an optical fiber that is injected into monochromatic linear polarized light. The direction of the electric field vector with respect to the Frenet frame of a pseudo-null curve determines the state polarization of a monochromatic linearly polarized light wave traveling along an optical fiber. For the Frenet frame of a

Swampland Conjectures have attracted quite some interest in the Cosmological Community. They have been shown to have wide ranging implications, like constraints on inflationary models, primordial black holes, etc. to name a few. A particularly revealing insight on dark energy also shows that one can have the dark energy equation-of-state for a quintessence scenario to be significantly different than

In this paper, as an application of the inverse problem of calculus of variations, we investigate two compatibility conditions on the spherically symmetric Finsler metrics. By making use of these conditions, we focus our attention on the Landsberg spherically symmetric Finsler metrics. We classify all spherically symmetric manifolds of Landsberg or Berwald types. For the higher dimensions n≥3, we prove

In this work, we show that semi-Riemannian group manifold admits Ricci solitons and satisfies the dynamical cosmology equation of spacetime. In Sec. 2, we introduce and provide some geometric properties of semisymmetric nonmetric connection in semi-Riemannian space. In Sec. 3, we define and show some geometric properties of group manifold endowed with semisymmetric nonmetric connection in semi-Riemannian

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces

In this paper, we studied the generalized space and time fractional Korteweg–de Vries (KdV) equation in the sense of the Riemann–Liouville fractional derivative. Initially, the symmetry of this considered equation through the symmetry analysis method was obtained. Next, a one-parameter Lie group of point transformation was yielded. Then, this considered fractional model can be translated into an ordinary

Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent

The algebraic properties of a strict deformation quantization are analyzed on the classical phase space ℝ2n. The corresponding quantization maps enable us to take the limit for ℏ→0 of a suitable sequence of algebraic vector states induced by ℏ-dependent eigenvectors of several quantum models, in which the sequence converges to a probability measure on ℝ2n, defining a classical algebraic state. The

In this paper, we introduce k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a GRW spacetime. Using these curvatures, we establish some inequalities for lightlike hypersurfaces of a GRW spacetime. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We also get Chen–Ricci inequality and Chen inequality on a screen homothetic lightlike hypersurfaces

In this paper, model of gravitational collapse of anisotropic compact stars in a new theory of f(R) gravity has been developed. The author considers the modified gravity model of f(R)=ξR4 to investigate a physically acceptable model of gravitational collapse of anisotropic compact stars. First, the author presents a brief review of the development of field equations of gravitational collapse in f(R)

In this paper, we propose a model to describe the geometry of quantum correlations and entanglement through their distinct physical significance in quantum information processing and modern communications. However, geometric discord, using trace, Hilbert–Schmidt distances, and entanglement of formation, is engineered to be a well-defined non-classical correlation measure of an atomic field system.

In the framework of f(T)-gravity theory, classical and quantum cosmology has been studied in this work for Friedmann Lemaitre Robertson Walker Metric (FLRW) space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian, is used to the physical system and a specific functional form of f(T) is determined. A point transformation in the 2D augmented space restricts one of the variables

In this paper, the formal structure of Penrose’s gravitationally induced reduction of the wave function mechanism is analyzed. It is shown that pushing Penrose’s argument forward leads to the interpretation of quantum coherence in microscopic systems as an observable signature violation of general covariance. We discuss potential avenues to avoid this conclusion, among them emergent quantum mechanics

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, (GR)n structure are completely classified in this short report. A conformally flat generalized Ricci recurrent pseudo-Riemannian manifold is shown to be an Einstein manifold. In particular, a conformally flat generalized Ricci recurrent spacetime must be either a de Sitter spacetime or an anti-de Sitter spacetime.

The aim of this paper is to extend the notion of all known quasi-Einstein (QE) manifolds like generalized QE, mixed generalized QE manifold, pseudo generalized QE manifold and many more and name it comprehensive QE manifold Co(QE)n. We investigate some geometric and physical properties of the comprehensive QE manifolds Co(QE)n under certain conditions. We study the conformal and conharmonic mappings

In this paper, we demonstrate the application of non-commutative space-time algebra of sedeons to generalize the system of equations describing heat transfer and impurity diffusion in solids at finite velocity. It is shown that by analogy with electrodynamics, these transfer processes can be described using a compact second-order sedeonic equation for generalized scalar and vector potentials. On the

The main scope of this paper is to examine null Cartan curves especially the ones with constant torsion. In accordance with this scope, the position vector of a null Cartan curve is stated by a linear combination of the vector fields of its pseudo-orthogonal frame with differentiable functions. However, the most important difference that distinguishes this study from the other studies is that the Bertrand

In this paper, we investigate the cosmic acceleration and the behavior of dark energy (DE) in the structure of the recently proposed κ(R,T) gravity theory [G. R. P. Teruel, κ(R,T) gravity, Eur. Phys. J. C78 (2018) 660]. In this study, we obtained some fascinating cosmological features that are coherent with observational evidences and the touchstone ΛCDM model. To find the deterministic solution, we

In this paper, we define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Due to these softer requirements, transformations allowed by spin frames are more general than usual spin transformations and they usually do not preserve the induced

Based on the gravity model as a gauge theory previously by the authors, the introduction of noncommutative structures in the very geometry is discussed and developed in a new different way. Taking into account a linear Lagrangian in curvature and considering a pair of coherent vectors responsible, among other things, for the symmetry breaking, the introduction of noncommutativity in the very structure

This paper analyzes the constraint structure of a class of degenerate second-order particle Lagrangian that includes chiral oscillator, noncommutative oscillator, and two examples from reduced topologically massive gravity. For even-dimensional configuration spaces with maximal nondegeneracy, Dirac bracket is defined solely by coefficient field of highest derivative whereas for odd dimensions almost

In this work, we study the Rényi holographic dark energy (RHDE) model in a flat FRW Universe where the infrared cut-off is taken care by the Hubble horizon and also by taking three different parametrizations of the interaction term between the dark matter and the dark energy. Analyzing graphically, the behavior of some cosmological parameters in particular deceleration parameter, equation of state

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of f(ℛ,𝒯μν𝒯μν) gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine

Following the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedures, for classical dynamics within the Lagrangian and the Hamilton–Jacobi formalism.

In this paper, using the first law of thermodynamics (FLT), we derive a modification of the Friedmann equation from the nonadditive Tsallis entropy associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe, where matter inside the apparent horizon is represented by a scalar field with a potential. We suggest that the inflationary era of the universe may phenomenologically

The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi–Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev–Popov quantization approach, the anti-BRST invariance reflects thoroughly the classical symmetry of the Yang–Mills theories with respect to gauge fixing methods. The Nakanishi–Lautrup

In this paper, we study the construction of classical geometry from the quantum entanglement structure by using information geometry. In the information geometry of classical spacetime, the Fisher information metric is related to a blurred metric of a classical physical space. We first show that a local information metric can be obtained from the entanglement contour in a local subregion. This local

In this paper, we study the Rényi holographic dark energy (HDE) model in the context of the Chern–Simons (CS) model of modified gravity theory. Different cosmological parameters, such as energy density, deceleration parameter, equation of state, square of sound speed and cosmological plane, are discussed using the Friedmann–Lemaître–Robertson–Walker spacetime background. Two separate solutions of CS

In this paper, we present a theorem which explains the necessary onditions for parallel surfaces of null scrolls to be surfaces again. Then, we give some properties of parallel ruled surfaces such as the frame fields in terms of the original base curve’s frame vectors, the cases of cross products of these frames’ vector fields. Also, we show the parallel ruled surfaces to be developable from a different

In this paper, we study the collapse of a thin dust shell from the point of view of the horizon dynamics. We identify the critical surfaces at which time and space coordinates interchange their roles and investigate their properties by using the formalism of trapped surfaces. We show the existence of marginally outer trapped surfaces that are associated with the presence of quasi-local horizons. A

We present a rigidity result in Lorentzian geometry, related to Bartnik’s conjecture, under the hypothesis of the existence of a concircular vector field with certain properties. We also study the relationship between two different notions of concircular vector fields found in the literature, and give conditions for a generalized Robertson–Walker spacetime to have a timelike concircular vector field

In the framework of f(P) gravity, we examine the nature of cosmological parameters by choosing different models of f(P) gravity at past, present as well as future epoch for Hubble parameter from parameterized deceleration parameters. It is found that equation of state parameter leads to quintessence behavior and its ranges lie within Planck data for different constraints. We also study the squared

In this paper, Radiative Correction (RC) to the Casimir energy was computed for the self-interacting massive/massless Lifshitz-like scalar field, confined between a pair of plates with Dirichlet and Mixed boundary conditions in 3+1 dimensions. Moreover, using the results obtained for the Dirichlet Casimir energy, the RC to the Casimir energy for Periodic and Neumann boundary conditions were also draw

The Vaidya–Bonner metric is a non-static generalization of Reissner–Nordström metric and this paper deals with the investigation of the curvature restricted geometric properties of such a metric. The scalar curvature vanishes and several pseudosymmetric-type curvature conditions are fulfilled by this metric. Also, it is a 2-quasi-Einstein, Ein(3) and generalized Roter type manifold. As a special case

We study the f(R,T) cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case f(R,T)=f1(R)+f2(T) and the case f(R,T)=f1(R)+f2(R)f3(T). In each case, we state general theorems

In this work, we focus on the phase space singularities of interactive quintessence model in the presence of matter fluid. This model is related to swampland studies, that the outcomes affect all these swampland-related models with the same dynamical system. We shall form the dynamical system corresponding to the cosmological system, which is eventually autonomous, and by using the dominant balances

In this paper, we have investigated the physical behavior of cosmological models in modified Teleparallel gravity with a general function f(T)=αT+β(−T)n where α,β and n are model parameters and T is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. We have derived the deceleration parameter q(ω,H(z)) in terms of equation of state (EoS) parameter

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the

This analysis explores the solutions for wormhole in f(R,φ,χ) gravity, where χ,φ, and R represent the kinetic term, scalar potential, and Ricci scalar, respectively. For this study, we use the spherically symmetric spacetime with the anisotropic source of matter. Further, we use the linear equation of state to complete this current investigation in the background of conformal symmetry motion. By plugging

This work is aimed at the study of traversable wormholes, proposed by Morris and Thorne [Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395], in the framework of f(R,T)=R+αRn+λT gravity, where α, λ and n are constants. The wormhole solutions are obtained and analyzed by using a simplest form of shape function. Further, the

In this study, we addressed the influence of quantum singularity on the topological state. The quantum singularity creates the defect in the momentum space ubiquitously and leads to the phase transition for the topological material. The kinetic equation reveals that the defect generates an anomaly without the characteristic energy scale. In the holographic model, the three-dimensional dislocations

In this paper, we start the investigation of a new natural approach to “unifying” noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional (AF) C∗-algebras. The defining inductive sequence of an AFC∗-algebra is lifted to enable the construction of a sequence of NCGFT of Yang–Mills–Higgs types. This paper focuses on derivation-based noncommutative field theories. A mathematical

In this study, the analytical solutions of the Klein–Gordon equation for any l states of the modified effective mass potential under the modified unequal scalar and vector Coulomb–Hulthén potential (MUSVCH-P) are derived by using an approximation method to the centrifugal potential term in the symmetries of relativistic noncommutative three-dimensional real space (RNC: 3D-RS). The new analytical expressions

In this paper, we examine the embedded wormhole solutions in the modified f(ℛ,T) theory of gravity, where T denotes the trace of the energy–momentum tensor and ℛ is the Ricci scalar. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the

In this work, we develop a novel method to obtain numerical solution of well-known Korteweg–de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie group methods. This paper is a first attempt to

The aim of this paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson–Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with