Isoparametric submanifolds in two-dimensional complex space forms

被引：2

作者：

Carlos Diaz-Ramos, Jose ^{[1
]}

Dominguez-Vazquez, Miguel ^{[2
]}

Vidal-Castineira, Cristina ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Dept Math, Santiago De Compostela, Spain

[2] ICMAT Inst Ciencias Matemat CSIC UAM UC3M UCM, Madrid, Spain

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2018年 / 53卷 / 02期

关键词：

Complex hyperbolic plane; Complex projective plane; Isoparametric submanifold; Polar action; principal curvatures; CONSTANT PRINCIPAL CURVATURES; REAL HYPERSURFACES; FOLIATIONS;

D O I：

10.1007/s10455-017-9572-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos', is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng's. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms.

引用

页码：205 / 216

页数：12

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