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

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