The space of associated metrics on a symplectic manifold
نویسنده
چکیده
In this work the spaces of Riemannian metrics on a closed manifold M are studied. On the space M of all Riemannian metrics on M the various weak Riemannian structures are defined and the corresponding connections are studied. The space AM of associated metrics on a symplectic manifold M,ω is considered in more detail. A natural parametrization of the space AM is defined. It is shown, that AM is a complex manifold. A curvature of the spaceAM and quotient spaceAM/Dω is found. The spaces AM in cases when M is a two-dimensional sphere and two-dimensional torus are considered as application of general results. The critical metrics of the functional of the scalar curvature on AM are considered. The finite dimensionality of the space of associated metrics of a constant scalar curvature with Hermitian Ricci tensor is shown. ∗Kemerovo State University, Kemerovo, 650043, RUSSIA. Email [email protected],
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تاریخ انتشار 2008