The Gauss map of submanifolds in spaces of constant curvature (Q1893421)
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scientific article; zbMATH DE number 770002
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Gauss map of submanifolds in spaces of constant curvature |
scientific article; zbMATH DE number 770002 |
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The Gauss map of submanifolds in spaces of constant curvature (English)
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31 July 1995
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The author investigates the Gauss map of submanifolds in space forms that was defined by \textit{T. J. Willmore} and \textit{B. A. Saleemi} [J. Lond. Math. Soc. 41, 153-160 (1966; Zbl 0136.429)]. By using Morse functions, he shows that the degree of the Gauss map is the Euler number of the submanifold. He also relates it to tight immersion (i.e. minimal total absolute curvature) of submanifolds in space forms.
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parallel displacement
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space forms
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Morse functions
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Gauss map
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tight immersion
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