Bi-invariant metric on the strict contactomorphism group

A right-invariant metric $ρ_α$ on the compactly supported identity component $Cont_0(M,α)$ of the group of contactomorphisms of an arbitrary contact manifold $(M,α)$ 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 $ρ_α$ to the subgroup $G(M,α)$ of all strict contactomorphisms in $Cont_0(M,α)$ is bi-invariant.

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