Invariants of Immersions on n-Dimensional Affine Manifold

被引：0

作者：

Khadjiev, Djavvat ^{[1
]}

Beshimov, Gayrat ^{[1
]}

Oren, Idris ^{[2
]}

机构：

[1] Uzbek Acad Sci, VI Romanovsky Inst Math, Natl Univ Uzbekistan, Tashkent 100125, Uzbekistan

[2] Karadeniz Tech Univ, Fac Sci, Dept Math, TR-61080 Trabzon, Turkiye

来源：

GAZI UNIVERSITY JOURNAL OF SCIENCE | 2024年 / 37卷 / 02期

关键词：

Connection; Riemannian curvature; tensor; Invariant; ISOMETRIC IMMERSIONS; DIFFERENTIAL INVARIANTS; RIEMANNIAN SPACE; RECOVERY;

D O I：

10.35378/gujs.1037048

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Main results: The system of Christoffel symbols of the connection of an immersion 4.: 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 4 . , 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 4.: 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.

引用

页码：924 / 937

页数：14

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