Sub-Riemannian geometries on compact homogeneous spaces

被引：1

作者：

Gorbatsevich, V. V. ^{[1
]}

机构：

[1] Moscow State Univ Aviat Technol, Moscow, Russia

来源：

IZVESTIYA MATHEMATICS | 2014年 / 78卷 / 03期

关键词：

invariant distribution; sub-Riemannian structure; homogeneous space; SEMISIMPLE FUNDAMENTAL GROUP;

D O I：

10.1070/IM2014v078n03ABEH002694

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider totally non-holonomic sub-Riemannian structures on compact homogeneous spaces and conjecture that, in most cases, the existence of such a structure implies that there is an invariant Riemannian structure. We prove a strengthened version of this conjecture for some important classes of compact homogeneous spaces.

引用

页码：459 / 474

页数：16

共 50 条

[1] Sub-Riemannian Homogeneous Spaces of Engel Type
D. M. Almeida
[J]. Journal of Dynamical and Control Systems, 2014, 20 : 149 - 166
[2] Sub-Riemannian Homogeneous Spaces of Engel Type
Almeida, D. M.
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2014, 20 (02) : 149 - 166
[3] On invariant sub-Riemannian structures on compact homogeneous spaces with discrete stationary subgroup
Gorbatsevich, V. V.
[J]. MATHEMATICAL NOTES, 2014, 95 (5-6) : 768 - 774
[4] On invariant sub-Riemannian structures on compact homogeneous spaces with discrete stationary subgroup
V. V. Gorbatsevich
[J]. Mathematical Notes, 2014, 95 : 768 - 774
[5] Sub-Riemannian homogeneous spaces in dimensions 3 and 4
Falbel, E
Gorodski, C
[J]. GEOMETRIAE DEDICATA, 1996, 62 (03) : 227 - 252
[6] Homogeneous geodesics in sub-Riemannian geometry*
Podobryaev, Alexey
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2023, 29 : 1473 - 1483
[7] Curvatures of homogeneous sub-Riemannian manifolds
Berestovskii V.N.
[J]. European Journal of Mathematics, 2017, 3 (4) : 788 - 807
[8] Model spaces in sub-Riemannian geometry
Grong, Erlend
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2021, 29 (01) : 77 - 113
[9] ON CONTACT SUB-RIEMANNIAN SYMMETRICAL SPACES
FALBEL, E
GORODSKI, C
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 1995, 28 (05): : 571 - 589
[10] Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane
Yu. L. Sachkov
[J]. Differential Equations, 2021, 57 : 1550 - 1554

← 1 2 3 4 5 →