期刊
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
卷 49, 期 -, 页码 23-42出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2016.07.002
关键词
Volume preserving immersions; Sobolev metrics; Well-posedness; Geodesic equation
资金
- Erwin Schrodinger Institute programme: Infinite-Dimensional Riemannian Geometry with Applications to Image Matching and Shape Analysis
- FWF-project [P24625]
- Austrian Science Fund (FWF) [P 24625] Funding Source: researchfish
- Austrian Science Fund (FWF) [P24625] Funding Source: Austrian Science Fund (FWF)
Given a compact manifold M and a Riemannian manifold N of bounded geometry, we consider the manifold Imm(M, N) of immersions from M to N and its subset Imm mu(M, N) of those immersions with the property that the volume-form of the pull-back metric equals mu . We first show that the non-minimal elements of Imm mu(M,N) form a splitting submanifold. On this submanifold we consider the Levi-Civita connection for various natural Sobolev metrics, we write down the geodesic equation for which we show local well-posedness in many cases. The question is a natural generalization of the corresponding well-posedness question for the group of volume-preserving diffeomorphisms, which is of importance in fluid mechanics. (C) 2016 Elsevier B.V. All rights reserved.
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