Space of orthogonal complex structures
= Space of orthogonal complex structures
{title2=$O(2n)/U(n)$}
On a Euclidean real space of dimension $2n$, an orthogonal <complex structure> is an orthogonal endomorphism $J$ with $J^2=-I$. Orthogonal changes of basis act transitively on these structures, and the stabilizer of the standard structure is $U(n)$. The compact <homogeneous space> has real dimension $n(n-1)$.
// Target: geometry-and-topology.bigb