An extension of Chern-Lashof theorem to other space forms (Q2752849)
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scientific article; zbMATH DE number 1665586
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extension of Chern-Lashof theorem to other space forms |
scientific article; zbMATH DE number 1665586 |
Statements
21 October 2001
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Chern-Lashof theorem
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total Betti number
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Riemannian manifold
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central projection
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isometric immersion
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An extension of Chern-Lashof theorem to other space forms (English)
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The Chern-Lashof inequality states that the total absolute curvature of a compact submanifold in the Euclidean space is bounded from below by the total Betti number. The author obtains an extension of Chern-Lashof's inequality to other spaces and is able to give many interesting applications. An extension of the Fenchel-Borsuk inequality to spheres and hyperbolic spaces is given among other applications.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00035].
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