Bi-invariant metrics on the group of symplectomorphisms

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dc.creatorHan, Zhigang
dc.date2005-10-26
dc.date.accessioned2026-07-07T06:47:57Z
dc.date.available2026-07-07T06:47:57Z
dc.descriptionThis paper studies the extension of the Hofer metric and general Finsler metrics on Hamiltonian symplectomorphism group $Ham(M,ω)$ to the identity component $Symp_0(M,ω)$ of symplectomorphism group. In particular, we prove that the Hofer metric on $Ham(M,ω)$ does not extend to a bi-invariant metric on $Symp_0(M,ω)$ for many symplectic manifolds. We also show that for the torus $T^{2n}$ with the standard symplectic form $ω$, no Finsler metric on $Ham(T^{2n},ω)$ that satisfies a strong form of the invariance condition can extend to a bi-invariant metric on $Symp_0(T^{2n},ω)$. Another interesting result is that there exists no $C^1$-continuous bi-invariant metric on $Symp_0(T^{2n},ω)$.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0510569
dc.identifierhttp://arxiv.org/abs/math/0510569
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103824
dc.subjectSymplectic Geometry
dc.subject53D99;57R17
dc.titleBi-invariant metrics on the group of symplectomorphisms
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