Bi-invariant metric on the strict contactomorphism group

Abstract

A right-invariant metric ${\rho }_{\alpha }$ on the compactly supported identity component $Con{t}_0(M,\alpha )$ 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 $Con{t}_0(M,\alpha )$ is bi-invariant.

The paper has been withdrawn by the author.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