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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

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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