In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann–Christoffel curvature tensor, the same type structures given by imposing same restriction on other curvature tensors being studied. The main object of the present paper is to study the equivalency of various geometric structures obtained by same restriction imposing on different curvature tensors. In this purpose we present a tensor by combining Riemann–Christoffel curvature tensor, Ricci tensor, the metric tensor and scalar curvature which describe various curvature tensors as its particular cases. Then with the help of this generalized tensor and using algebraic classification we prove the equivalency of different geometric structures (see Theorems 6.3, 6.4, 6.5, 6.6 and 6.7; Tables 1 and 2).

On equivalency of various geometric structures

The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.

On a generalized class of recurrent manifolds

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.

Curvature Properties of Gödel metric

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 \(R\cdot R = Q(S,R)\), \(C\cdot C = \frac{2a^2}{3} Q(g,C)\), and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between Godel spacetime and Som–Raychaudhuri spacetime.

On curvature properties of Som–Raychaudhuri spacetime

We introduce a new curvature tensor named as the T-curvature ten- sor We show that the quasi-conformal, conformal, conharmonic, concircular, pseudo-projective, projective, M-projective, Wi-curvature tensors (i =0 ,, 9), W ∗ -curvature tensors (j =0 , 1) are the particular cases of the T-curvature tensor Some properties for the T-curvature tensor are given We obtain the results for T-conservative and T-flat semi-Riemannian manifolds

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S Uysal Aynur

Papers

On conharmonic transformations of weyl spaces