Isoparametric hypersurfaces with four or six distinct principal curvatures
@article{Abresch1983IsoparametricHW, title={Isoparametric hypersurfaces with four or six distinct principal curvatures}, author={Uwe Abresch}, journal={Mathematische Annalen}, year={1983}, volume={264}, pages={283-302} }
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110 Citations
Isoparametric hypersurfaces with four principal curvatures, II
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Abstract In this sequel to an earlier article, employing more commutative algebra than previously, we show that an isoparametric hypersurface with four principal curvatures and multiplicities (3,4)…
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In [6], employing commutative algebra, we showed that if the number of principal curvatures is 4 and if the multiplicities m1 and m2 of the principal curvatures satisfy m2 ≥ 2m1 − 1, then the…
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The classification of isoparametric hypersurfaces with four principal curvatures in the sphere interplays in a deep fashion with commutative algebra, whose abstract and comprehensive nature might…
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A hypersurface M n 1 in a real space-form R n , S n or H n is isoparametric if it has constant principal curvatures. For R n and H n , the classification of isoparametric hypersurfaces is complete…
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We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair $(7,8)$ is either the one constructed by Ozeki and Takeuchi, or one of the two constructed by Ferus,…
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Abstract. Let M be a Dupin hypersurface in the unit sphere
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Abstract.All known examples of isoparametric hypersurfaces of spheres are of the following two types:¶(1) The homogeneous examples, which are principal orbits of isotropy representations of symmetric…
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This is a survey of the closely related fields of taut submanifolds and Dupin submanifolds of Euclidean space. The emphasis is on stating results in their proper context and noting areas for future…
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