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arXiv · 1402.0967

Bi-invariant metric on contact 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 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.

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N. K. Smolentsev. 2014-02-05. Bi-invariant metric on contact diffeomorphisms group. https://arxiv.org/abs/1402.0967

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