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

作　　者：张留伟[1] 李兴校[2] 贾志刚[1] 

机构地区：[1]信阳师范学院数学与信息科学学院 [2]河南师范大学数学与信息科学学院

出　　处：《河南师范大学学报（自然科学版）》2010年第4期33-35,共3页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10671181)

摘　　要：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}^⊥.

关 键 词：NEARLY Khler流形 KILLING向量场 闭2次形式 

分 类 号：O186.16[理学—数学]