Abstract
We consider conformal and concircular mappings of Eisenhart’s generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart’s generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart’s generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.
Highlights
A non-symmetric basic tensor was used by several authors as the main axiom of the theory which is nowdays called a non-symmetric gravitational theory [1]
We describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds
In the present paper we studied conformal and concircular mappings of generalized Riemannian spaces without any of the restrictive assumptions and find some tensors that are invariant with respect to these mappings
Summary
A non-symmetric basic tensor was used by several authors as the main axiom of the theory which is nowdays called a non-symmetric gravitational theory [1]. Reference [2] formally introduced a generalized Riemannian space as a differentiable manifold endowed with a non-symmetric basic tensor. References [3,4] found new curvature tensors of a non-symmetric linear connection. In the papers [22,23] and the papers that follow these ones, the authors studied conformal and concircular mappings of generalized Riemannian spaces with assumption that these mappings were preserving the torsion tensor. In the present paper we studied conformal and concircular mappings of generalized Riemannian spaces without any of the restrictive assumptions and find some tensors that are invariant with respect to these mappings. We define some new kinds of symmetric spaces with torsion by taking into account five curvature tensors of Eisenhart’s generalized Riemannian spaces and four kinds of covariant derivative
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