Invariants of Immersions on n-Dimensional Affine Manifold
Gazi University Journal of Science, cilt.37, sa.2, ss.924-937, 2024 (ESCI, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 37 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.35378/gujs.1037048
- Dergi Adı: Gazi University Journal of Science
- Derginin Tarandığı İndeksler: 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)
- Sayfa Sayıları: ss.924-937
- Anahtar Kelimeler: Connection, Invariant, Riemannian curvature, tensor
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
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.