On submanifolds with negative curvature in Euclidean space (Q1758343)
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scientific article; zbMATH DE number 6104268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On submanifolds with negative curvature in Euclidean space |
scientific article; zbMATH DE number 6104268 |
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On submanifolds with negative curvature in Euclidean space (English)
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9 November 2012
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From the abstract and the introduction: In this paper we give a survey of results of different authors, among them Tenenblat's, on the behavior of submanifolds with negative curvature. The following topics are considered, each more or less connected with the question of existence of submanifolds with negative curvature bounded away from zero: (a) Some constructions of submanifolds with negative curvature. (b) On the regularity of the image of a Bäcklund transformation. (c) On the Grassmannian image of an immersion. (d) The expression for the volume of an asymptotic parallelepiped.
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negative curvature
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regularity
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volume
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asymptotic coordinates
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Lobachevsky space
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isometric immersion
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