Bi-invariant metric on contact diffeomorphisms group

Abstract

We show the existence of a weak bi-invariant symmetric nondegenerate 2-form on the contact diffeomorphisms group ${\mathcal{D}}_{\theta }$ of a contact Riemannian manifold $(M,g,\theta )$ and study its properties. We describe the Euler's equation on a Lie algebra of group ${\mathcal{D}}_{\theta }$ and calculate the sectional curvature of ${\mathcal{D}}_{\theta }$. In a case $\dim M=3$ connection between the bi-invariant metric on ${\mathcal{D}}_{\theta }$ and the bi-invariant metric on volume-preserving diffeomorphisms group ${\mathcal{D}}_{\mu }$ of $M^3$ is discover.

12 pages

References in corpus (2)

• Riemannian geometry on the quantomorphism group
• Bi-invariant metric on volume-preserving diffeomorphisms group of a three-dimensional manifold

Cited by in corpus (1)

• Bi-invariant metric on symplectic diffeomorphisms group