具有处处非零Killing向量场的nearly Khler流形

Nearly Khler Manifolds with Some Nowhere Vanishing Killing Vector Fields

研究了在nearly Khler流形上某种处处非零Killing向量场的存在性与流形的拓扑和几何之间的联系.并且得到了下面的主要结论及其推论:设(M2n,g,J)是一个2n维的近复流形.如果在M上存在一个处处非零的Killing向量场ξ,使得ξ*∧Jξ*是闭2次形式,则M局部微分同胚于M1×M2,其中M1和M2分别是分布V∶=span{ξ,Jξ}和分布H:=span{ξ,Jξ}⊥的极大积分子流形.

This research mainly studies the relation between the existence of some nowhere vanishing Killing vector fields on nearly Khler manifold and the topology and geometry of the manifold. The main result and it＇s corollary can be improved： Let （M^2n,g,J）be a 2n-dimensional almost complexmanifold. If there exists a nowhere vanishing Killing vector field ξ on M such that ξ^＊∧Jξ^＊ is a closed 2-form, then M is locally diffeomorphic to M1×M2, where M1 and M2 are maximum integral submanifolds of distributions V∶=span{ξ,Jξ} and H∶=span{ξ,Jξ}^⊥.