Conditions for the Parallelism of the Normal Curvature Tensor of Submanifolds

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 276; no. 6; pp. 695 - 700
• Main Author: Bodrenko, I. I.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.11.2023; Springer; Springer Nature B.V
• Subjects: Curvature; Manifolds (mathematics); Mathematical analysis; Mathematics; Mathematics and Statistics; Tensors; space of constant curvature; 53C40; 53B25; submanifold; second fundamental form; normal torsion vector; normal curvature tensor; normal curvature vector
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-023-06793-4

In this paper, sufficient conditions for the parallelism of the normal curvature tensor of submanifolds in spaces of constant curvature are obtained. Keywords and phrases: submanifold, space of constant curvature, second fundamental form, normal curvature tensor, normal curvature vector, normal tors...