SUB-RIEMANNIAN GEOMETRY OF STIEFEL MANIFOLDS

被引：6

作者：

Autenried, Christian ^{[1
]}

Markina, Irina ^{[1
]}

机构：

[1] Univ Bergen, Dept Math, N-5020 Bergen, Norway

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2014年 / 52卷 / 02期

关键词：

sub-Riemannian geometry; normal geodesic; cut locus; Stiefel manifolds; Grassmann manifold; METRICS; CONSTRAINTS; ALGORITHMS;

D O I：

10.1137/130922537

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In the paper we consider the Stiefel manifold V-n,V- k as a principal U(k)-bundle over the Grassmann manifold and study the cut locus from the unit element. We give the complete description of this cut locus on V-n,V- 1 and present a sufficient condition on the general case. At the end, we study the complement to the cut locus of V-2k,V- k.

引用

页码：939 / 959

页数：21

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