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

共 50 条

[1] Isoparametric submanifolds in two-dimensional complex space forms
José Carlos Díaz-Ramos
Miguel Domínguez-Vázquez
Cristina Vidal-Castiñeira
Annals of Global Analysis and Geometry, 2018, 53 : 205 - 216
[2] COMPLEX SUBMANIFOLDS OF INDEFINITE COMPLEX SPACE FORMS
Cheng, Xiaoliang
Hao, Yihong
Yuan, Yuan
Zhang, Xu
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (06) : 2541 - 2550
[3] Certain submanifolds of complex space forms
Mirjana Djorić
Masafumi Okumura
São Paulo Journal of Mathematical Sciences, 2021, 15 : 111 - 126
[4] Certain submanifolds of complex space forms
Djoric, Mirjana
Okumura, Masafumi
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2021, 15 (01): : 111 - 126
[5] Focal sets in two-dimensional space forms
Arturo Escudero, Carlos
Reventos, Agusti
Solanes, Gil
PACIFIC JOURNAL OF MATHEMATICS, 2007, 233 (02) : 309 - 320
[6] EXAMPLES OF INFINITE DIMENSIONAL ISOPARAMETRIC SUBMANIFOLDS
PINKALL, U
THORBERGSSON, G
MATHEMATISCHE ZEITSCHRIFT, 1990, 205 (02) : 279 - 286
[7] Homogeneity of infinite dimensional isoparametric submanifolds
Heintze, E
Liu, XB
ANNALS OF MATHEMATICS, 1999, 149 (01) : 149 - 181
[8] Biwarped product submanifolds of complex space forms
Khan, Meraj Ali
Khan, Kamran
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2019, 16 (05)
[9] Classification of slumbilical submanifolds in complex space forms
Chen, BY
OSAKA JOURNAL OF MATHEMATICS, 2002, 39 (01) : 23 - 47
[10] Generic submanifolds of generalized complex space forms
Tripathi, MM
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1997, 50 (3-4): : 373 - 392

← 1 2 3 4 5 →