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.

Keywords

• conformal mapping
• Eisenhart’s generalized Riemannian space
• Weyl conformal tensor
• Yano’s concircular curvature
• symmetric space