Laguerre characterization of some hypersurfaces (Q2812481)
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scientific article; zbMATH DE number 6594408
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Laguerre characterization of some hypersurfaces |
scientific article; zbMATH DE number 6594408 |
Statements
16 June 2016
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Laguerre geometry
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Laguerre hypersurface
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Laguerre form
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Laguerre scalar curvature
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Laguerre characterization of some hypersurfaces (English)
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The present article classifies hypersurfaces in \(\mathbb R^n\) which are free of umbilics, have non-zero principal curvatures and parallel Laguerre form, and whose trace-free Laguerre tensor is bounded by a constant times the Laguerre scalar curvature. The main result states that locally only two types of hypersurfaces are possible. Both already appeared in similar classification results, for example in [\textit{T. Li} et al., Sci. China, Math. 54, No. 6, 1129--1144 (2011; Zbl 1246.53016)].
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