Showing papers by "Doddabhadrappla Gowda Prakasha published in 2017"
14 Feb 2017
TL;DR: In this article, the authors considered a projective curvature tensor on Lorentzian and Sasakian manifolds and showed that the curvatures are projectively flat and semisymmetric.
Abstract: We consider $${\mathcal {M}}$$
-projective curvature tensor on Lorentzian $$\alpha $$
- Sasakian manifolds and show that $${\mathcal {M}}$$
-projectively semisymmetric Lorentzian $$\alpha $$
-Sasakian manifold is $${\mathcal {M}}$$
-projectively flat. Further, it is shown that, $${\mathcal {M}}$$
-projectively semisymmetric Lorentzian $$\alpha $$
-Sasakian manifold is semisymmetric. Finally, some results related to energy momentum tensor satisfying the Einstein field equation with cosmological constant of the $${\mathcal {M}}$$
-projectively semisymmetric Lorentzian $$\alpha $$
-Sasakian space-times are investigated.
6 citations
01 Aug 2017
TL;DR: In this article, the authors studied the nature of Lorentzian-Sasakian manifold admitting M -projective curvature tensors and showed that the curvatures of these tensors are locally isometric to unit sphere.
Abstract: In this paper, we study the nature of Lorentzian -Sasakian manifolds admitting M -projective curvature tensor. We show that M -projectively flat and irrotational M -projective curvature tensor of Lorentzian -Sasakian manifolds are locally isometric to unit sphere ) (c S n , where 2 = c . Next we study Lorentzian -Sasakian manifold with conservative M -projective curvature tensor. Finally, we find certain geometrical results if the Lorentzian -Sasakian manifold satisfying the relation 0 = ) , ( R Y X M .