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

共 50 条

[21] Mass Transportation on Sub-Riemannian Manifolds
Alessio Figalli
Ludovic Rifford
[J]. Geometric and Functional Analysis, 2010, 20 : 124 - 159
[22] On isometric immersions of sub-Riemannian manifolds
Rovenski, Vladimir
[J]. FILOMAT, 2023, 37 (25) : 8543 - 8551
[23] Isometries of complemented sub-Riemannian manifolds
Hladky, Robert K.
[J]. ADVANCES IN GEOMETRY, 2014, 14 (02) : 319 - 352
[24] Quasiregular Mappings on Sub-Riemannian Manifolds
Faessler, Katrin
Lukyanenko, Anton
Peltonen, Kirsi
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2016, 26 (03) : 1754 - 1794
[25] Curvatures of homogeneous sub-Riemannian manifolds
Berestovskii V.N.
[J]. European Journal of Mathematics, 2017, 3 (4) : 788 - 807
[26] Sub-Riemannian geometry and nonholonomic mechanics
Bejancu, Aurel
[J]. ALEXANDRU MYLLER MATHEMATICAL SEMINAR, 2011, 1329 : 16 - 25
[27] Model spaces in sub-Riemannian geometry
Grong, Erlend
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2021, 29 (01) : 77 - 113
[28] Homogeneous geodesics in sub-Riemannian geometry*
Podobryaev, Alexey
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2023, 29 : 1473 - 1483
[29] Characteristic Laplacian in Sub-Riemannian Geometry
Daniel, Jeremy
Ma, Xiaonan
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (24) : 13290 - 13323
[30] Sub-Riemannian geometry of parallelizable spheres
Molina, Mauricio Godoy
Markina, Irina
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2011, 27 (03) : 997 - 1022

← 1 2 3 4 5 →