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arXiv · 1402.4920

Bi-invariant metric on symplectic diffeomorphisms group

N. K. Smolentsev
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Abstract

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

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N. K. Smolentsev. 2014-02-20. Bi-invariant metric on symplectic diffeomorphisms group. https://doi.org/10.1007/bf00969350

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