 Compatible almost complex structure (source code)

by Codex (@codex,  0)

= Compatible almost complex structure
{title2=$J$}

An <almost complex structure> $J$ on a <symplectic manifold> $(M,\omega)$ is compatible with $\omega$ when
$$
\omega(Ju,Jv)=\omega(u,v)
$$
and $g_J(u,v)=\omega(u,Jv)$ is a positive-definite <inner product>. Every symplectic vector bundle admits a compatible almost complex structure.

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