广义递归抛物空间拟测地线映射的基本定理

Q3 Mathematics
Irina Kurbatova, Margaret Pistruil, Nadiia Konovenko
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引用次数: 0

摘要

在以前的文章中,我们研究了伪黎曼空间相互拟测地线和几乎第二类测地线的映射。得到具有仿射结构的空间的拟测地线映射f: (Vn, gij, Fih)→(Vn, gij, Fih),称为广义循环映射。拟测地线映射分为一般映射和正则映射两种类型。本文研究了广义递归抛物空间的拟测地线映射理论的基本问题。首先,准测地线映射的基本方程被简化为一种允许有效研究的形式。然后,利用基本方程的一种新形式,证明了存在广义递归抛物空间(Vn, gij, Fih)的定理,或者证明了存在广义递归抛物空间(Vn, gij, Fih)的定理,或者证明了不存在广义递归抛物空间(Vn, gij, Fih)的定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fundamental theorems of quasi-geodesic mappings of generalized-recurrent-parabolic spaces
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.
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来源期刊
Proceedings of the International Geometry Center
Proceedings of the International Geometry Center Mathematics-Geometry and Topology
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
3 weeks
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