Submanifolds with parallel Ricci tensor (Q1110111)
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scientific article; zbMATH DE number 4071848
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Submanifolds with parallel Ricci tensor |
scientific article; zbMATH DE number 4071848 |
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Submanifolds with parallel Ricci tensor (English)
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1988
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The author gives a classification of submanifolds of a Riemannian manifold of constant sectional curvature having parallel Ricci tensor, parallel mean curvature vector field and trivial normal connection. A corollary is the classification of 2-codimensional Einstein submanifolds of a Riemannian manifold of constant sectional curvature having parallel mean curvature vector field. It is shown that the submanifolds in question have parallel second fundamental form. The proof of Theorem 1 as it is written in the paper seems to be incomplete but the lacking arguments can be supplied rather easily.
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parallel Ricci tensor
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parallel mean curvature vector
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normal connection
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Einstein submanifolds
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0.9844122
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0.93057334
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0.9281268
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