Finiteness results for equifocal hypersurfaces in compact symmetric spaces

Jian Quan Ge; Chao Qian

doi:10.1007/s11425-013-4753-3

Finiteness results for equifocal hypersurfaces in compact symmetric spaces

Jian Quan Ge, Chao Qian^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Moreover, if the symmetric space is of rank one, the result can be strengthened by dropping the condition curvature-adapted.

Original language	English
Pages (from-to)	1975-1982
Number of pages	8
Journal	Science China Mathematics
Volume	57
Issue number	9
DOIs	https://doi.org/10.1007/s11425-013-4753-3
Publication status	Published - Sept 2014
Externally published	Yes

Keywords

equifocal hypersurface
finiteness
focal point
isoparametric hypersurface

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10.1007/s11425-013-4753-3

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title = "Finiteness results for equifocal hypersurfaces in compact symmetric spaces",

abstract = "We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Moreover, if the symmetric space is of rank one, the result can be strengthened by dropping the condition curvature-adapted.",

keywords = "equifocal hypersurface, finiteness, focal point, isoparametric hypersurface",

author = "Ge, {Jian Quan} and Chao Qian",

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AU - Qian, Chao

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AB - We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Moreover, if the symmetric space is of rank one, the result can be strengthened by dropping the condition curvature-adapted.

KW - equifocal hypersurface

KW - finiteness

KW - focal point

KW - isoparametric hypersurface

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DO - 10.1007/s11425-013-4753-3

M3 - Article

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EP - 1982

JO - Science China Mathematics

JF - Science China Mathematics

IS - 9

ER -

Finiteness results for equifocal hypersurfaces in compact symmetric spaces

Abstract

Keywords

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