On generalized projective <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si11.svg"><mml:mi mathvariant="script">P</mml:mi></mml:math>-curvature tensor

De, Uday Chand; Abu-Donia, H. M.; Shenawy, Sameh; Syied, Abdallah Abdelhameed

doi:10.1016/j.geomphys.2020.103952

Cited by 6 publications

(3 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An invariant orthogonal decomposition of the covariant derivative of the Ricci tensor was coined and studied by Gray in [7] (see also [8][9][10]). e manifolds in the trivial subspace have parallel Ricci tensor; that is, ∇ k R ij � 0. e subspace A contains manifolds whose Ricci tensor is Killing; that is,…”

Section: Introductionmentioning

confidence: 99%

Investigation of Pseudo-Ricci Symmetric Spacetimes in Gray’s Subspaces

Shenawy

Turki

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

In the present paper, we focused our attention to study pseudo-Ricci symmetric spacetimes in Gray’s decomposition subspaces. It is proved that PRS n spacetimes are Ricci flat in trivial, A , and B subspaces, whereas perfect fluid in subspaces I , I ⊕ A , and I ⊕ B , and have zero scalar curvature in subspace A ⊕ B . Finally, it is proved that pseudo-Ricci symmetric GRW spacetimes are vacuum, and as a consequence of this result, we address several corollaries.

show abstract

Section: Introductionmentioning

confidence: 99%

Investigation of Pseudo-Ricci Symmetric Spacetimes in Gray’s Subspaces

Shenawy

Turki

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…e Weyl curvature tensor describes the distorting but volume-preserving tidal effects of gravitation on a material body. e P−curvature tensor was first coined by De et al in 2021 [2]. is curvature tensor is a good generalization of projective [3], conharmonic [4], M−projective [5], and the set of W i −curvature tensors which was introduced by Pokhariyal and Mishra [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…is curvature tensor is a good generalization of projective [3], conharmonic [4], M−projective [5], and the set of W i −curvature tensors which was introduced by Pokhariyal and Mishra [6][7][8][9][10]. is curvature tensor is given by P ijkl � a 0 R ijkl + a 1 g ij R kl + a 2 g ik R jl + a 3 g il R jk + a 4 g jk R il + a 5 g jl R ik + a 6 g kl R ij , (1) where a i are constants, R ijkl is the Riemann tensor, and R ij is the Ricci tensor [2]. e authors studied this curvature tensor on pseudo-Riemannian manifolds and space times of general relativity.…”

Section: Introductionmentioning

confidence: 99%

A Study of Generalized Projective $P -$ Curvature Tensor on Warped Product Manifolds

Syied

Turki

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

The main aim of this study is to investigate the effects of the P − curvature flatness, P − divergence-free characteristic, and P − symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P − curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P − curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P − divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P − symmetric warped product manifold is considered.

show abstract