Invariants of Immersions on n-Dimensional Affine Manifold

Authors : Djavvat Khadjiev, Gayrat Beshimov, İdris Ören

Pages : 924-937

Doi:10.35378/gujs.1037048

View : 63 | Download : 95

Publication Date : 2024-06-01

Article Type : Research Paper

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.
Keywords : Connection, Riemannian curvature tensor, Invariant