On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

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.

Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold

“…Moreover, the Einstein tensor can be obtained from Yano's tensor of concircular curvature. In [11], by using this approach, some generalizations of the Einstein tensor were achieved.…”

Conformal Equitorsion and Concircular Transformations in a Generalized Riemannian Space

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