Fundamental theorems of quasi-geodesic mappings of generalized-recurrent-parabolic spaces

Abstract

In previous papers we studied mappings of pseudo-Riemannian spaces being mutually quasi-geodesic and almost geodesic of the 2nd type. As a result, we arrived at the quasi-geodesic mapping f: (Vn, gij, Fih) → (Vn, gij, Fih) of spaces with an affine structure, which was called generalized-recurrent. Quasi-geodesic mappings are divided into two types: general and canonical. In this article, the fundamental issues of the theory of quasi-geodesic mappings of generalized-recurrent-parabolic spaces are considered. First, the fundamental equations of quasi-geodesic mappings are reduced to a form that allows effective investigation. Then, using a new form of the fundamental equations, we prove theorems that allow for any generalized-recurrent-parabolic space (Vn, gij, Fih) or to find all spaces (Vn, gij, Fih) onto which Vn admits a quasi-geodesic mapping of the general form, or prove that there are no such spaces.

Keywords

• affine structure
• quasi-geodesic mapping
• pseudo-riemannian space