Abstract
In this paper, we define a (0,2)-type symmetric tensor Z and called it a generalized Z tensor. We study weakly cyclic generalized Z-symmetric manifold and prove that it is a generalized quasi-Einstein manifold. We have obtained a condition for vanishing of sum of 1-forms. We further find a condition to be a Ricci semisymmetric manifold. Finally, it is shown that the semisymmetry and Weyl semisymmetry are equivalent in such a manifold.
This is a preview of subscription content, log in via an institution to check access.
References
Mantica CA, Molinari LG (2012) Weakly Z-symmetric manifolds. Acta Math Hung 135(1):80–96
Mantica CA, Suh YJ (2012) Pseudo Z-symmetric Riemannian manifolds with harmonic curvature tensors. Int J Geom Methods Mod Phys 9(1):1250004
Mantica CA, Suh YJ (2012) Recurrent Z-forms on Riemannian and Kähler manifold. Int J Geom Methods Mod Phys 9(7):1250059
Mantica CA, Suh YJ (2014) Pseudo Z-symmetric space-times. J Math Phys 55:042502
De UC, Mantica CA, Suh YJ (2015) On weakly cyclic Z-symmetric manifolds. Acta Math Hung 146(1):153–167
Chern SS (1956) On the curvature and characteristic classes of a Riemannian manifold. Abh Math Sem Univ Hambg 20:117–126
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pandey, P. On Weakly Cyclic Generalized Z-Symmetric Manifolds. Natl. Acad. Sci. Lett. 43, 347–350 (2020). https://doi.org/10.1007/s40009-020-00875-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40009-020-00875-6
Keywords
- Generalized Z tensor
- Generalized quasi-Einstein manifold
- Weyl semisymmetry
- Conformally flat manifold
- Generalized quasi-constant curvature