Bauer, Martin and Michor, Peter W. and Mueller, Olaf (2016) Riemannian geometry of the space of volume preserving immersions. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 49. pp. 23-42. ISSN 0926-2245, 1872-6984
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SOBOLEV METRICS; SHAPE SPACE; EQUATION; EPDIFF; MOTION; WHIPS; Volume preserving immersions; Sobolev metrics; Well-posedness; Geodesic equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Apr 2019 12:36 |
| Last Modified: | 10 Apr 2019 12:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3895 |
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