Bi-invariant metric on the strict contactomorphism group

Details Bi-invariant metric on the strict contactomorphism group Bi-invariant metric on the strict contactomorphism group

2012-02-27

arxiv.org/abs/1202.5897v2

Mathematics

Differential Geometry

The paper has been withdrawn by the author. The bi-invariant metric is correctly defined, but some statements in the proof are

Scientific paper

A right-invariant metric $\rho_{\alpha}$ on the compactly supported identity component $Cont_0(M,\alpha)$ of the group of contactomorphisms of an arbitrary contact manifold $(M,\alpha)$ is introduced in a similar way that the Hofer metric was defined on the group of Hamiltonian symplectomorphisms of a symplectic manifold. The restriction of $\rho_{\alpha}$ to the subgroup $G(M,\alpha)$ of all strict contactomorphisms in $Cont_0(M,\alpha)$ is bi-invariant.

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