Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci tensors upto level 2. The object of the present paper is to investigate the cha…
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15 results for “Roter”
Defines a new tensor related to special geometric spaces.
problem Understanding new curvature tensors in semi-Riemannian geometry.
method Defines a generalized curvature tensor using specific operations.
result The tensor is connected to quasi-Einstein, Roter, and Roter-type spaces.
We determine a particular class of Roter type warped product manifolds. We show that every manifold of that class admits a geodesic mapping onto a some Roter type warped product manifold. Moreover, both geodesically related manifolds are pseudosymmetric of constant type.
The main object of the present paper is to study the geometric properties of a generalized Roter type semi-Riemannian manifold, which arose in the way of generalization to find the form of the Riemann-Christoffel curvature tensor . Again for a particular curvature restriction on and the Ricci tensor there ar…
Study of hypersurfaces in curved spaces with specific curvature properties.
problem Characterizing hypersurfaces in spaces of constant curvature with particular curvature properties.
method Investigates hypersurfaces isometrically immersed in semi-Riemannian spaces of constant curvature, focusing on the curvature tensor and its properties.
result Hypersurfaces in the specified spaces satisfy a Roter type equation, linking their curvature tensor to specific tensor products.
This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with -dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in gen…
On pseudosymmetric manifoldsmath.DG
In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […
Som-Raychaudhuri 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 …
The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate hypersurfaces M in space forms N satisfying (A). The main result states that if the ten…
The curvature properties of Robinson-Trautman metric have been investigated. It is shown that Robinson-Trautman metric admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Also it is shown that the difference $R…
Investigates geometric properties of Bardeen black hole spacetime.
problem Examines curvature properties of Bardeen black hole spacetime.
method Analyzes pseudosymmetry, pseudosymmetric Weyl curvature, and recurrent structures.
result Bardeen spacetime is a manifold of pseudosymmetry Weyl curvature and satisfies special recurrent like structure.
Compact ECS manifolds are proven to be bundles over the circle.
problem Compact ECS manifolds and their local structure.
method Proof of a specific result for compact rank-one ECS manifolds.
result Compact rank-one ECS manifolds, not locally homogeneous, are bundles over the circle.
Compact ECS manifolds have a simple topological structure.
problem Understanding the structure of compact ECS manifolds.
method Review of basic facts, construction of examples, and proof of a topological structure result.
result Compact rank-one ECS manifolds are bundles over S^1 with fibers being leaves of D⊥.
Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.
problem Exploring geometric properties of Vaidya-Bonner-de Sitter spacetime.
method Analyzing conformal curvature, conharmonic curvature, and other curvatures.
result VBdS spacetime exhibits various pseudosymmetric structures and geometric features.
The paper examines geometric properties of a specific black hole spacetime.
problem Curvature properties of a Hayward black hole spacetime.
method Analyzes the curvature properties of Hayward black hole spacetime using Einstein field equations.
result The Hayward black hole spacetime is an Einstein manifold and exhibits various types of pseudosymmetry.