On the problem of geodesic mappings and deformations of generalized Riemannian spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Najdanovic, Marija S.^1,2 

[1] Univ Nis, Fac Sci & Math, Nish 18000, Serbia

[2] Presch Teacher Training Coll, Krusevac 37000, Serbia

关键词: Geodesic mapping;    Infinitesimal deformation;    Infinitesimal geodesic deformation;    Generalized Riemannian space;    Generalized equidistant space;   

DOI  :  10.1016/j.jmaa.2017.02.069

来源: Elsevier

【 摘 要 】

This paper is devoted to a study of geodesic mappings and infinitesimal geodesic deformations of generalized Riemannian spaces. While a geodesic mapping between two generalized Riemannian spaces any geodesic line of one space sends to a geodesic line of the other space, under an infinitesimal geodesic deformation any geodesic line is mapped to a curve approximating a geodesic with a given precision. Basic equations of the theory of geodesic mappings in the case of generalized Riemannian spaces are obtained in this paper. A new generalization of the famous Levi Civita's equation is found. Necessary and sufficient conditions for a nontrivial infinitesimal geodesic deformation are given. It is proven that a generalized Riemannian space admits nontrivial infinitesimal geodesic deformations if and only if it admits nontrivial geodesic mappings. At last it is shown that generalized equidistant spaces of primary type admit nontrivial geodesic deformations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free