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VOL. 18 | 2017 Geodesic Mappings Onto Riemannian Manifolds and Differentiability
Irena Hinterleitner, Josef Mikeš

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka

## Abstract

In this paper we study fundamental equations of geodesic mappings of manifolds with affine connection onto (pseudo-)Riemannian manifolds. We proved that if a manifold with affine (or projective) connection of differentiability class $C^r (r\geq2)$ admits a geodesic mapping onto a (pseudo-)Riemannian manifold of class $C^1$, then this manifold belongs to the differentiability class $C^{r+1}$. From this result follows if an Einstein spaces admits non-trivial geodesic mappings onto (pseudo-)Riemannian manifolds of class $C^1$ then this manifold is an Einstein space, and there exists a common coordinate system in which the components of the metric of these Einstein manifolds are real analytic functions.

## Information

Published: 1 January 2017
First available in Project Euclid: 14 January 2017

zbMATH: 1378.53025
MathSciNet: MR3616920

Digital Object Identifier: 10.7546/giq-18-2017-183-190