期刊
IZVESTIYA MATHEMATICS
卷 77, 期 3, 页码 541-570出版社
TURPION LTD
DOI: 10.1070/IM2013v077n03ABEH002648
关键词
robust infinite-dimensional weak Riemannian manifolds; curvature in terms of the cometric; right-invariant Sobolev metrics on diffeomorphism groups; O'Neill's formula; manifold of submanifolds
类别
资金
- ONR [N00014-09-1-0256]
- FWF-project [21030]
- NSF [DMS-0704213, DMS-0456253]
Given a finite-dimensional manifold N, the group Diff(S)(N) of diffeomorphisms of N which decrease suitably rapidly to the identity, acts on the manifold B(M, N) of submanifolds of N of diffeomorphism-type M, where M is a compact manifold with dim M < dim N. Given the right-invariant weak Riemannian metric on DiffS(N) induced by a quite general operator L: (sic)(S)(N) -> (T* N circle times vol(N)), we consider the induced weak Riemannian metric on B(M, N) and compute its geodesics and sectional curvature. To do this, we derive a covariant formula for the curvature in finite and infinite dimensions, we show how it makes O'Neill's formula very transparent, and we finally use it to compute the sectional curvature on B(M, N).
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据