On the submanifolds of the Riemannian manifolds (Q2723977)
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scientific article; zbMATH DE number 1615314
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the submanifolds of the Riemannian manifolds |
scientific article; zbMATH DE number 1615314 |
Statements
8 July 2001
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principal direction
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principal curvature
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canonical normal vector
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normal curvature
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osculator space
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On the submanifolds of the Riemannian manifolds (English)
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The author introduces principal directions and principal normal vectors of an arbitrary \(n\)-dimensional submanifold of an \((n+k)\)-dimensional Riemannian space so that they depend on the embedding of the submanifold. He states the condition when the principal directions and the principal curvatures are intrinsic. Moreover, the author introduces the canonical normal vectors and curvatures for submanifolds of Riemannian spaces, which do not depend on the parametrization of the submanifold.
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