Moduli space of symplectic connections of Ricci type on $T^{2n}$; a formal approach

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dc.creatorCahen, M.
dc.creatorGutt, S.
dc.creatorHorowitz, J.
dc.creatorRawnsley, J.
dc.date2002-01-18
dc.date2002-02-08
dc.date.accessioned2026-07-07T04:45:56Z
dc.date.available2026-07-07T04:45:56Z
dc.descriptionWe consider analytic curves $\nabla^t$ of symplectic connections of Ricci type on the torus $T^{2n}$ with $\nabla^0$ the standard connection. We show, by a recursion argument, that if $\nabla^t$ is a formal curve of such connections then there exists a formal curve of symplectomorphisms $ψ_t$ such that $ψ_t\cdot\nabla^t$ is a formal curve of flat invariant symplectic connections and so $\nabla^t$ is flat for all $t$. Applying this result to the Taylor series of the analytic curve, it means that analytic curves of symplectic connections of Ricci type starting at $\nabla^0$ are also flat. The group $G$ of symplectomorphisms of the torus $(T^{2n},ω)$ acts on the space $\E$ of symplectic connections which are of Ricci type. As a preliminary to studying the moduli space $\E/G$ we study the moduli of formal curves of connections under the action of formal curves of symplectomorphisms.
dc.descriptionLaTeX, 19 pages. Removed claim to handle all symplectic structures on the torus
dc.identifierhttps://arxiv.org/abs/math/0201167
dc.identifierhttp://arxiv.org/abs/math/0201167
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63143
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.titleModuli space of symplectic connections of Ricci type on $T^{2n}$; a formal approach
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