Differential geometry of complex and almost complex manifolds

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The Kobayashi hyperbolicity is also defined for almost complex manifolds. Though analytical proofs of locally complete hyperbolicity for almost complex manifolds were known, we obtained a new differential geometric one. The moment map of Kaehler manifolds are important since it is involved with the problem of stability. It is extended to the analogous one for almost Kaehler manifolds. We found that it becomes simpler in a sense for the almost Kaehler manifolds, since one does not need the integrability conditions.