Cohomogeneity one actions on noncompact symmetric spaces of rank one

被引：71

作者：

Berndt, Juergen ^{[1
]}

Tamaru, Hiroshi

机构：

[1] Natl Univ Ireland Univ Coll Cork, Dept Math, Cork, Ireland

[2] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 359卷 / 07期

关键词：

symmetric spaces; hyperbolic spaces; cohomogeneity one actions; homogeneous hypersurfaces;

D O I：

10.1090/S0002-9947-07-04305-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n >= 3. For the quaternionic hyperbolic spaces HHn, n >= 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classi. cation problem was essentially solved by Elie Cartan.

引用

页码：3425 / 3438

页数：14