On warped product manifolds satisfying some curvature conditions

Chojnacka-Dulas, J; Deszcz, Ryszard; Głogowska, Małgorzata; Prvanović, Mileva

doi:10.1016/j.geomphys.2013.08.007

Cited by 38 publications

(55 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let U S = {x ∈ M : S − r n g x = 0}. Then the manifold is said to be quasiEinstein [14,19,25,28,39,40,43,49,56,69,88,94,105] if on U S ⊂ M , we have…”

Section: Preliminariesmentioning

confidence: 99%

Curvature properties of some 4-dimensional semi-Riemannian metrics

A.¹,

Matsuyama²

2017

Kragujevac J Math

View full text Add to dashboard Cite

show abstract

“…Let U S = {x ∈ M : S − r n g x = 0}. Then the manifold is said to be quasiEinstein [14,19,25,28,39,40,43,49,56,69,88,94,105] if on U S ⊂ M , we have…”

Section: Preliminariesmentioning

confidence: 99%

Curvature properties of some 4-dimensional semi-Riemannian metrics

A.¹,

Matsuyama²

2017

Kragujevac J Math

View full text Add to dashboard Cite

show abstract

“…S = α g + ε w ⊗ w, for some α ∈ R, where ε = ±1 and w is a non-zero covector at p. It is known that quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations and investigation on quasi-umbilical hypersurfaces of conformally flat spaces (e.g. see [18,26], and references therein). An extension of the class of Einstein semi-Riemannian manifolds form manifolds with parallel Ricci tensor S, i.e.…”

Section: Some Generalized Einstein Metric Conditionsmentioning

confidence: 99%

“…see [18,26,27,38,42,51,65,70], and references therein). In particular, [65] contains results on quasi-Einstein manifolds satisfying curvature conditions involving the conharmonic tensor conh(R).…”

Section: Notationsmentioning

confidence: 99%

On Chen Ideal Submanifolds Satisfying Some Conditions of Pseudo-symmetry Type

Deszcz

Petrović–Torgašev

Verstraelen

et al. 2015

Bull. Malays. Math. Sci. Soc.

View full text Add to dashboard Cite

In this paper, we study Chen ideal submanifolds M n of dimension n in Euclidean spaces E n+m (n ≥ 4, m ≥ 1) satisfying curvature conditions of pseudosymmetry type of the form: the difference tensor R · C − C · R is expressed by some Tachibana tensors. Precisely, we consider one of the following three conditions: R ·C −C · R is expressed as a linear combination of Q(g, R) and Q(S, R), R ·C −C · R is expressed as a linear combination of Q(g, C) and Q(S, C) and R · C − C · R is expressed as a linear combination of Q(g, g∧S) and Q(S, g∧S). We then characterize Dedicated to the memory of Professor Franki Dillen. Communicated by Young Jin Suh. B Miroslava Petrović-Torgasev mirapt@kg.ac.rs Ryszard Deszcz Ryszard.Deszcz@up.wroc.pl

show abstract

“…A semi-Riemannian manifold (M, g), n 3, is said to be Ricci-symmetric if ∇R = 0 holds on M. It is obvious that the last condition leads immediately to the integrability condition (6). Manifolds satisfying (6) are called Ricci-semisymmetric.…”

Section: Preliminariesmentioning

confidence: 99%

“…Such warped products are called generalized Robertson-Walker spacetimes ([1], [30], [44]). Curvature conditions of pseudosymmetry type on such spacetimes have been considered among others in [6,7,8,10,27,28,29,33,39].…”

Section: Warped Product Manifoldsmentioning

confidence: 99%

On generalized Robertson--Walker spacetimes satisfying some curvaturecondition

Arslan¹,

Deszcz²,

Ezentaş³

et al. 2014

Turk J Math

View full text Add to dashboard Cite

We give necessary and sufficient conditions for warped product manifolds (M, g) , of dimension ⩾ 4 , with 1 -dimensional base, and in particular, for generalized Robertson-Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the difference tensor R•C −C •R , formed from the curvature tensor R and the Weyl conformal curvature tensor C , is expressed by the Tachibana tensor Q(S, R) formed from the Ricci tensor S and R . We also construct suitable examples of such manifolds. They are quasi-Einstein, i.e. at every point of M rank (S − α g) ⩽ 1 , for some α ∈ R , or non-quasi-Einstein.

show abstract

On warped product manifolds satisfying some curvature conditions

Cited by 38 publications

References 24 publications

Curvature properties of some 4-dimensional semi-Riemannian metrics

Curvature properties of some 4-dimensional semi-Riemannian metrics

On Chen Ideal Submanifolds Satisfying Some Conditions of Pseudo-symmetry Type

On generalized Robertson--Walker spacetimes satisfying some curvaturecondition

Contact Info

Product

Resources

About