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''Hodge manifold''

A [[Complex manifold|complex manifold]] on which a Hodge metric can be given, that is, a [[Kähler metric|Kähler metric]] whose fundamental form defines an integral cohomology class. A compact complex manifold is a Hodge manifold if and only if it is isomorphic to a smooth algebraic subvariety of some complex projective space (Kodaira's projective imbedding theorem).

See also [[Kähler manifold|Kähler manifold]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  P.A. Griffiths,   J.E. Harris,   "Principles of algebraic geometry" , '''1''' , Wiley  (1978)</TD></TR></table>