Differential geometry of complex and almost complex manifolds

对于几乎复流形，还定义了小林双曲性。虽然已有关于几乎复流形的局部完全双曲性的分析证明，但我们得到了一个新的微分几何性质。由于Kaehler流形的矩映射涉及稳定性问题，因此它是非常重要的。将其推广到几乎Kaehler流形上的类似情形。我们发现，几乎Kaehler流形在某种意义上变得更简单，因为人们不需要可积性条件。

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.