Totally Geodesic Submanifolds and Polar Actions on Stiefel Manifolds

被引：0
|
作者：
Gorodski, Claudio [1 ]
Kollross, Andreas [2 ]
Rodriguez-Vazquez, Alberto [3 ]
机构：
[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil
[2] Univ Stuttgart, Inst Geometrie & Topol, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
[3] Univ Libre Bruxelles, Dept Math, Blvd Triomphe,CP 218, B-1050 Brussels, Belgium
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2025年 / 35卷 / 02期
基金：
巴西圣保罗研究基金会; 瑞典研究理事会;
关键词：
Stiefel manifolds; Totally geodesic; Polar actions; Cohomogeneity one; SYMMETRIC-SPACES; CLASSIFICATION; COMPLEX;
D O I：
10.1007/s12220-024-01855-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove that the orbits of polar actions are lifts of polar actions on the corresponding Grassmannian. In the case of cohomogeneity one actions we are able to obtain a classification for all real, complex and quaternionic Stiefel manifolds of k-frames.
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页数：21
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