Bi-invariant metric on symplectic diffeomorphisms group

Abstract

We show the existence of a weak bi-invariant symmetric nondegenerate 2-form on the symplectic diffeomorphisms group ${\mathcal{D}}_{\omega }$ of a symplectic Riemannian manifold $(M,g,\omega )$ and study its properties. We describe the Euler's equation on a Lie algebra of group ${\mathcal{D}}_{\omega }$ and calculate the sectional curvature of ${\mathcal{D}}_{\omega }(T^n)$.

12 pages

References in corpus (2)

• Bi-invariant metric on volume-preserving diffeomorphisms group of a three-dimensional manifold
• Bi-invariant metric on contact diffeomorphisms group