On the space of almost complex structures

Abstract

The space $\mathcal{A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space $\mathcal{A}$ is defined. It is shown, that $\mathcal{A}$ is a infinite dimensional complex weak Pseudo-Riemannian manifold. A curvature of the space $\mathcal{A}$ is found. The space ${\mathcal{A}}_{\omega }$ of associated almost complex structures on a symplectic manifold $M,\omega$ and space $\mathcal{A}O$ of orthogonal almost complex structures on a Riemannian manifold $M,g_0$ are considered in more detail.

LaTeX, 8 pages