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Riemannian geometry of the space of volume preserving immersions

Bauer, Martin ; Michor, Peter W. ; Müller, Olaf



Abstract

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 ...

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