High Quality Content by WIKIPEDIA articles! In mathematics, a Kahler manifold is a manifold with unitary structure (a U(n)-structure) satisfying an integrability condition. In particular, it is a Riemannian manifold, a complex manifold, and a symplectic manifold, with these three structures all mutually compatible.Without any integrability conditions, the analogous notion is an almost Hermitian manifold. If the Sp-structure is integrable (but the complex structure need not be), the notion is an almost Kahler manifold; if the complex structure is integrable (but the Sp-structure need not be), the notion is a Hermitian manifold.

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