Invariants of Immersions on n-Dimensional Affine Manifold

IF 1 Q3 MULTIDISCIPLINARY SCIENCES

gazi university journal of science Pub Date : 2023-11-03 DOI:10.35378/gujs.1037048

D. Khadjiev, Gayrat Beshi̇mov, İdris Ören

引用次数: 0

Abstract

Main results: The system of Christoffel symbols of the connection of an immersion ξ:J→R^n of an n-dimensional manifold J in the n-dimensional linear space R^n is a system of generators of the differential field of all Aff(n)-invariant differential rational functions of ξ, where Aff(n) is the group of all affine transformations of R^n. A similar result have obtained for the subgroup SAff(n) of ⁡Aff(n) generated by all unimodular linear transformations and parallel translations of R^n. Rigidity and uniqueness theorems for immersions ξ:J→R^n in geometries of groups Aff(n) and SAff(n) were obtained. These theorems are given in terms of the affine connection and the volume form of immersions.

查看原文本刊更多论文

n 维仿射频域上的不变量

主要结果n 维流形 J 在 n 维线性空间 R^n 中的浸透ξ:J→R^n 的连接的克里斯托弗符号系统是ξ的所有 Aff(n) 不变微分有理函数的微分域的生成器系统，其中 Aff(n) 是 R^n 的所有仿射变换群。对于由 R^n 的所有单模态线性变换和平行平移产生的 Aff(n) 的子群 SAff(n) 也有类似的结果。我们还得到了浸没ξ:J→R^n 在 Aff(n) 和 SAff(n) 群几何中的刚性和唯一性定理。这些定理是根据浸入的仿射连接和体积形式给出的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

gazi university journal of science MULTIDISCIPLINARY SCIENCES-

CiteScore

1.60

自引率

11.10%

发文量

期刊介绍： The scope of the “Gazi University Journal of Science” comprises such as original research on all aspects of basic science, engineering and technology. Original research results, scientific reviews and short communication notes in various fields of science and technology are considered for publication. The publication language of the journal is English. Manuscripts previously published in another journal are not accepted. Manuscripts with a suitable balance of practice and theory are preferred. A review article is expected to give in-depth information and satisfying evaluation of a specific scientific or technologic subject, supported with an extensive list of sources. Short communication notes prepared by researchers who would like to share the first outcomes of their on-going, original research work are welcome.