Geodesic Mappings of Special Riemannian Manifolds

TL;DR

This paper studies geodesic mappings between special Riemannian manifolds, revealing new properties of Einstein, Ricci recurrent, and symmetric manifolds and their mappings.

Contribution

It introduces new results on geodesic mappings involving Einstein, Ricci recurrent, and pseudo Ricci symmetric manifolds, expanding understanding of their geometric relations.

Findings

Einstein tensor preserving geodesic mappings lead to nearly quasi Einstein manifolds.

New results on geodesic mappings of Ricci recurrent and Ricci symmetric manifolds.

Investigation of geodesic mappings for pseudo Ricci symmetric and almost pseudo Ricci symmetric manifolds.

Abstract

In this paper, we will investigate the geodesic mappings of some special Riemannian manifolds. First, we will prove that if there exists an Einstein tensor preserving geodesic mapping from a quasi Einstein manifold $V_{n}$ onto a Riemannian manifold $\bar{V}_{n}$, then $\bar{V}_{n}$ is nearly quasi Einstein. Furthermore, we will obtain new results concerning the geodesic mappings of Ricci recurrent and Ricci symmetric manifolds. Next, by using these results, we will investigate the geodesic mappings of pseudo Ricci symmetric and almost pseudo Ricci symmetric manifolds.