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arXiv · 1202.5897

Bi-invariant metric on the strict contactomorphism group

Tomasz Rybicki
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Abstract

A right-invariant metric $\rho_{\alpha}$ on the compactly supported identity component $Cont_0(M,\alpha)$ of the group of contactomorphisms of an arbitrary contact manifold $(M,\alpha)$ 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 $\rho_{\alpha}$ to the subgroup $G(M,\alpha)$ of all strict contactomorphisms in $Cont_0(M,\alpha)$ is bi-invariant.

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Tomasz Rybicki. 2012-02-27. Bi-invariant metric on the strict contactomorphism group. https://arxiv.org/abs/1202.5897

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