Geodesic
Curvature Properties of Generalized pp-Wave Metrics
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 2, p. 237

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a 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 $P\cdot P = -\frac{1}{3}Q(S, P)$. 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. Again 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.
Classification : 53B20, 53B30, 53B50, 53C25, 83C15
Keywords: Einstein field equations, Brinkmann-wave metric, pp-wave metric, generalized pp-wave metric, Robinson-Trautman metric, Einstein manifold, quasi-Einstein manifold, 2-quasi-Einstein manifold, generalized quasi-Einstein manifold in the sense of Chaki, recurrent type curvature condition, pseudosymmetry type curvature condition 
@article{KJM_2021_45_2_a6,
     author = {Absos Ali Shaikh and Tran Quoc Binh and Haradhan Kundu},
     title = {Curvature {Properties} of {Generalized} {pp-Wave} {Metrics}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {237 },
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_2_a6/}
}
TY  - JOUR
AU  - Absos Ali Shaikh
AU  - Tran Quoc Binh
AU  - Haradhan Kundu
TI  - Curvature Properties of Generalized pp-Wave Metrics
JO  - Kragujevac Journal of Mathematics
PY  - 2021
SP  - 237 
VL  - 45
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2021_45_2_a6/
LA  - en
ID  - KJM_2021_45_2_a6
ER  - 
%0 Journal Article
%A Absos Ali Shaikh
%A Tran Quoc Binh
%A Haradhan Kundu
%T Curvature Properties of Generalized pp-Wave Metrics
%J Kragujevac Journal of Mathematics
%D 2021
%P 237 
%V 45
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2021_45_2_a6/
%G en
%F KJM_2021_45_2_a6
Absos Ali Shaikh; Tran Quoc Binh; Haradhan Kundu. Curvature Properties of Generalized pp-Wave Metrics. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 2, p. 237 . http://geodesic.mathdoc.fr/item/KJM_2021_45_2_a6/