SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS

被引：4

作者：

Arguillere, Sylvain ^{[1
]}

Trelat, Emmanuel ^{[2
,3
]}

机构：

[1] Johns Hopkins Univ, Ctr Imaging Sci, Baltimore, MD 21218 USA

[2] UPMC Univ Paris 06, Sorbonne Univ, CNRS UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[3] Inst Univ France, F-75005 Paris, France

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2017年 / 16卷 / 04期

关键词：

group of diffeomorphisms; sub-Riemannian geometry; normal geodesics; abnormal geodesics; reachability; Moser theorems; SOBOLEV METRICS; EQUATIONS; SPACES;

D O I：

10.1017/S1474748015000249

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide examples of normal and of abnormal geodesics in that infinite-dimensional context. The momentum formulation gives a sub -Riemannian version of the Euler-Arnol'd equation. Finally, we establish some approximate and exact reachability properties for diffeomorphisms, and we give some consequences for Moser theorems.

引用

页码：745 / 785

页数：41

共 50 条

[21] Hypersurfaces and variational formulas in sub-Riemannian Carnot groups
Montefalcone, Francescopaolo
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (05): : 453 - 494
[22] Second Variation of Sub-Riemannian Surface Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups
Santos, Maria R. B.
Veloso, Jose M. M.
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2023, 29 (03) : 721 - 756
[23] Second Variation of Sub-Riemannian Surface Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups
Maria R. B. Santos
José M. M. Veloso
[J]. Journal of Dynamical and Control Systems, 2023, 29 : 721 - 756
[24] Sub-Riemannian (2, 3, 5, 6)-Structures
Yu. L. Sachkov
E. F. Sachkova
[J]. Doklady Mathematics, 2021, 103 : 61 - 65
[25] On Integrability of Certain Rank 2 Sub-Riemannian Structures
Kruglikov, Boris S.
Vollmer, Andreas
Lukes-Gerakopoulos, Georgios
[J]. REGULAR & CHAOTIC DYNAMICS, 2017, 22 (05): : 502 - 519
[26] Sub-Riemannian structures in a principal bundle and their Popp measures
Bauer, Wolfram
Furutani, Kenro
Iwasaki, Chisato
[J]. APPLICABLE ANALYSIS, 2017, 96 (14) : 2390 - 2407
[27] Sub-Riemannian geometry
Kupka, I
[J]. ASTERISQUE, 1997, (241) : 351 - 380
[28] Characterisation of the sub-Riemannian isometry groups of H-type groups
Tan, KH
Yang, XP
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2004, 70 (01) : 87 - 100
[29] On integrability of certain rank 2 sub-Riemannian structures
Boris S. Kruglikov
Andreas Vollmer
Georgios Lukes-Gerakopoulos
[J]. Regular and Chaotic Dynamics, 2017, 22 : 502 - 519
[30] Riemannian and Sub-Riemannian Geodesic Flows
Godoy Molina, Mauricio
Grong, Erlend
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2017, 27 (02) : 1260 - 1273

← 1 2 3 4 5 →