Absos Ali Shaikh

On pseudo quasi-Einstein manifolds

The object of the present paper is to introduce a type of non-flat semi-Riemannian manifold, called pseudo quasi-Einstein manifold and to study some geometric and global properties of such a manifold. Also the existence of such a manifold is ensured by several non-trivial examples.

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 LORENTZIAN QUASI-EINSTEIN MANIFOLDS

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.

SOME RESULTS ON (LCS)n-MANIFOLDS

The object of the present paper is to study (LCS)n-mani- folds. Several interesting results on a (LCS)n-manifold are obtained. Also the generalized Ricci recurrent (LCS)n-manifolds are studied. The existence of such a manifold is ensured by several non-trivial new exam- ples.

On decomposable weakly conharmonically symmetric manifolds

The object of the present paper is to study and classify decomposable weakly conharmonically symmetric manifolds with several nontrivial examples.

On the existence of a new class of semi-Riemannian manifolds

AbstractThe present paper deals with the existence of a new class of semi-Riemannian manifolds which are weakly generalized recurrent, pseudo quasi-Einstein and fulfill the condition R·R=Q(S,R). For this purpose, we presented a metric, computed its curvature properties, and finally checked various geometric structures arising out from the different curvatures by means of their covariant derivatives of first and second order.MCS53C15; 53C25; 53C35

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 GENERALIZED φ‐RECURRENT (LCS)n‐MANIFOLDS

R\cdot R = Q(S,R)