Geodesic
On the Manifold of Almost Complex Structures
Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 66-71.

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Let $(M,g_0)$ be a smooth closed Riemannian manifold of even dimension $2n$ admitting an almost complex structure. It is shown that the space $\mathscr A^+$ of all almost complex structures on $M$ determining the same orientation as the one determined by a fixed almost complex structure $J_0$ is a smooth locally trivial fiber bundle over the space $\mathscr A\mathscr O_{g_0}^+$ of almost complex structures orthogonal with respect to $g_0$ and determining the same orientation as $J_0$. 
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N. A. Daurtseva. On the Manifold of Almost Complex Structures. Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 66-71. http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a6/

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