On the space of almost complex structures

Details On the space of almost complex structures On the space of almost complex structures

2002-02-15

arxiv.org/abs/math/0202139v1

Vestnik KemGU ser. Matem. Vyp. 3(7) (2001) 176-185

Mathematics

Differential Geometry

LaTeX, 8 pages

Scientific paper

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 ${\mathcal AO}$ of orthogonal almost complex structures on a Riemannian manifold $M,g_0$ are considered in more detail.

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