Haradhan Kundu

Curvature properties of Gödel metric

The main aim of this paper is to investigate the geometric structures admitting by the Godel spacetime which produces a new class of semi-Riemannian manifolds. We also consider some extension of Godel metric.

On curvature properties of Som–Raychaudhuri spacetime

Som–Raychaudhuri (Proc R Soc Lond A 304:81–86, 1968) spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som–Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasi-Einstein, generalized Roter type, Ein(3) manifold satisfying

On equivalency of various geometric structures

R\cdot R = Q(S,R)

On warped product generalized Roter type manifold

R·R=Q(S,R),

On warped product manifolds satisfying some pseudosymmetric type conditions

C\cdot C = \frac{2a^2}{3} Q(g,C)

On the existence of a generalized class of recurrent manifolds

C·C=2a23Q(g,C), and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between Gödel spacetime and Som–Raychaudhuri spacetime.