Curvature properties of some 4-dimensional semi-Riemannian metrics

A., A. Shaikh; Matsuyama, Yoshio

doi:10.5937/kgjmath1702259s

Cited by 2 publications

(2 citation statements)

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“…The curvature properties of an warped product metric have also been investigated in [55] Thus, it is worthy to investigate the geometric structures of a warped product spacetime like Melvin of 3-dimensional base and 1-dimensional fibre.…”

Section: Introductionmentioning

confidence: 99%

Curvature properties of Melvin magnetic metric

Shaikh

Ali

Alkhaldi

et al. 2020

Journal of Geometry and Physics

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This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with 1-dimensional fibre.For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in general, is generalized Roter type, Ein(3) and has pseudosymmetric Weyl conformal tensor satisfying the pseudosymmetric type condition R · R − Q(S, R) = L ′ Q(g, C). The condition for which it satisfies the Roter type condition has been obtained. It is interesting to note that Melvin magnetic metric is pseudosymmetric and pseudosymmetric due to conformal tensor. Moreover such metric is 2-quasi-Einstien, its Ricci tensor is Reimann compatible and Weyl conformal 2-forms are recurrent. The Maxwell tensor is also pseudosymmetric type. 0 * Corresponding author.

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Section: Introductionmentioning

confidence: 99%

Curvature properties of Melvin magnetic metric

Shaikh

Ali

Alkhaldi

et al. 2020

Journal of Geometry and Physics

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“…Lanczos potentials of the metric are studied by Ahsan and Bilal [2]. In the study of differential geometry, pseudosymmetric structures play an important role due their applications in relativity and cosmology (see, [14], [30], [33], [36], [68], [76] and also references therein). It is noteworthy to mention that the present paper is unconventional as by considering a physically relevant metric, viz., Robinson-Trautman metric, we would like to investigate the curvature restricted geometric structures admitted by such metric.…”

Section: Introductionmentioning

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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Curvature properties of some 4-dimensional semi-Riemannian metrics

Cited by 2 publications

References 64 publications

Curvature properties of Melvin magnetic metric

Curvature properties of Melvin magnetic metric

Curvature properties of Robinson–Trautman metric

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