摘要
本文首先研究了殆Kaehler流形中CR子流形的上同调、CR子流形的分布D及其正交补D的可积性,这些研究是文献〔1〕、〔3〕、〔6〕及〔8〕中有关结果的推广。另外,当D的维数大于1的时候,近Kaehler流形中每个全脐非平凡的CR子流形一定是全测地的。最后得到:如果M是具有H_B>0的近Kaehler流形,那么M不允许有混合叶层非凡的CR子流形。
Studies are made of the cohomology of CR-submanifolds and the integrability of distributions D and D(?) of CR- submanifolds in an almost Kaehler manifold, as extensions of the results in [1] , [3] , [6] and [8] . Totally umbilical non-trivial CR-submanifolds in a nearly Kaehler manifold must be totally geodesic unless the dimensions of their orthogonal complement D(?) are not larger than I.
Finally, M admits no mixed foliate non-trivial CR-submanifolds if M is a nearly Kaehler manifold with HB>0 .
关键词
子流形
复流形
殆复流形
可积性
submanifolds
complex manifold
almost complex manifold
distribution
integral/totally umbilical submanifolds
