%0 Journal Article
%T The space of associated metrics on a symplectic manifold
%A N. K. Smolentsev
%J Mathematics
%D 2001
%I arXiv
%X The 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 $M,\omega$ 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 ${\mathcal AM}/{\mathcal D}_{\omega}$ is found. The finite dimensionality of the space of associated metrics of a constant scalar curvature with Hermitian Ricci tensor is shown.
%U http://arxiv.org/abs/math/0108110v1