Invariants of Immersions on n-Dimensional Affine Manifold

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Khadjiev D., Beshimov G., ÖREN İ.

Gazi University Journal of Science, vol.37, no.2, pp.924-937, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.35378/gujs.1037048
  • Journal Name: Gazi University Journal of Science
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.924-937
  • Keywords: Connection, Invariant, Riemannian curvature, tensor
  • Karadeniz Technical University Affiliated: Yes

Abstract

Main results: The system of Christoffel symbols of the connection of an immersion ξ:J→Rn of an n-dimensional manifold J in the n-dimensional linear space Rn 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 Rn. A similar result have obtained for the subgroup SAff(n) of Aff(n) generated by all unimodular linear transformations and parallel translations of Rn. Rigidity and uniqueness theorems for immersions ξ:J→Rn 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.