Bi-invariant metric on the strict contactomorphism group

2012/02/27 by Tomasz Rybicki, Rybicki, Tomasz
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1202.5897

openalex publication_date 2012/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A right-invariant metric ρ_α on the compactly supported identity component Cont₀(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 Cont₀(M,α) is bi-invariant.

Related

• Hofer metric from the contact point of view
• The Hofer norm of a contactomorphism
• Bi-invariant metric on contact diffeomorphisms group
• Bi-invariant metrics on the group of symplectomorphisms
• A new metric on the contactomorphism group of orderable contact manifolds