The symmetry of warped product space-times

Curvature properties of Gödel metric

“…However, the converse statement is not true. For instance, the Schwarzschild spacetime, the Kottler spacetime and the Reissner-Nordström spacetime satisfy (8) with nonzero function L R [55] (see also [56,57]). We also mention that Friedmann-Lemaître-Robertson-Walker spacetimes are pseudosymmetric (cf.…”

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

“…However, the converse statement is not true. For instance, the Schwarzschild spacetime, the Kottler spacetime and the Reissner-Nordström spacetime satisfy (5) with non-zero function L R [45] (see also [53]). The Schwarzschild spacetime was discovered in 1916 by K. Schwarzschild, during his study on solutions of Einstein's equations.…”

On some type of curvature conditions

“…Investigating the condition (30) we considered two cases: the quasi-Einstein case and the non-quasi-Einstein case and we obtained the following results. (30). Then on U the curvature tensor R is of the form (14), where µ (µ − (30).…”

“…We also mention that the metric of the Schwarzschild spacetime is a conformal deformation of some semisymmetric metric. The Schwarzschild spacetime, the Kottler spacetime as well as the Reissner-Nordström spacetime are nonsemisymmetric pseudosymmetric manifolds ( [14], [30]). In general, the Robertson-Walker spacetimes are pseudosymmetric.…”

“…The converse statement is not true. For instance, the Schwarzschild spacetime is a non-semisymmetric pseudosymmetric manifold ( [30]). In Section 4 we present results on pseudosymmetric manifolds.…”