The space of associated metrics on a symplectic manifold

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dc.creatorSmolentsev, N. K.
dc.date2001-08-16
dc.date.accessioned2026-07-07T04:42:59Z
dc.date.available2026-07-07T04:42:59Z
dc.descriptionThe spaces of Riemannian metrics on a closed manifold $M$ are studied. On the space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak Riemannian structures are defined and the corresponding connections are studied. The space ${\mathcal AM}$ of associated metrics on a symplectic manifold $M,ω$ is considered in more detail. A natural parametrization of the space ${\mathcal AM}$ is defined. It is shown, that ${\mathcal AM}$ is a complex manifold. A curvature of the space ${\mathcal AM}$ and quotient space ${\mathcal AM}/{\mathcal D}_ω$ is found. The finite dimensionality of the space of associated metrics of a constant scalar curvature with Hermitian Ricci tensor is shown.
dc.descriptionLaTeX, 83 pages
dc.identifierhttps://arxiv.org/abs/math/0108110
dc.identifierhttp://arxiv.org/abs/math/0108110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62027
dc.subjectDifferential Geometry
dc.subject58D17 (Primary) 53C15 (Secondary)
dc.titleThe space of associated metrics on a symplectic manifold
dc.typetext

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