Conditions for the Parallelism of the Normal Curvature Tensor of Submanifolds

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...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 276; no. 6; pp. 695 - 700
Main Author Bodrenko, I. I.
Format Journal Article
LanguageEnglish
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
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Summary: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 torsion vector. AMS Subject Classification: 53B25, 53C40
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06793-4