On Roter type warped products with 1-dimensional fibres

Deszcz, Ryszard; Plaue, Matthias; Scherfner, Mike

doi:10.1016/j.geomphys.2013.02.006

Cited by 33 publications

(19 citation statements)

References 16 publications

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“…Roter type manifolds and in particular Roter type hypersurfaces (i.e. hypersurfaces satisfying (2.9)), in semi-Riemannian spaces of constant curvature were studied in: [16,17,21,24,32,37,38,39,40,44,52]. Roter type manifolds satisfy several pseudosymmetry type curvature conditions, we have Theorem 2.1.…”

Section: Preliminary Resultsmentioning

confidence: 99%

On geodesic mappings in particular class of Roter spaces

Deszcz¹,

Hotloś²

2018

Preprint

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Section: Preliminary Resultsmentioning

confidence: 99%

On geodesic mappings in particular class of Roter spaces

Deszcz¹,

Hotloś²

2018

Preprint

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“…Roter spaces and in particular Roter hypersurfaces (i.e., hypersurfaces satisfying (2.9)) in semi-Riemannian spaces of constant curvature were studied in [12,13,16,19,30,31,32,36,44]. Roter spaces satisfy several pseudosymmetry type curvature conditions.…”

Section: )mentioning

confidence: 99%

On geodesic mappings in a particular class of Roter spaces

Deszcz

Hotloś

2021

Colloq. Math.

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“…Definition 2.4. A semi-Riemannian manifold M is said to be a Roter type manifold ( [18], [19], [23], [27], [35] and [39]) (resp., generalized Roter type manifold ( [22], [26], [28], [63], [66], [67] and [79])…”

Section: Definition 22 a Semi-riemannian Manifold Is Said To Be 2-qua...mentioning

confidence: 99%

Curvature properties of Robinson–Trautman metric

2018

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The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P · P = − 1 3 Q(S, P ). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent.Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. And the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

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On Roter type warped products with 1-dimensional fibres

Cited by 33 publications

References 16 publications

On geodesic mappings in particular class of Roter spaces

On geodesic mappings in particular class of Roter spaces

On geodesic mappings in a particular class of Roter spaces

Curvature properties of Robinson–Trautman metric

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