近切触流形的φ~*-解析向量场（英文）  

φ~*-ANALYTIC VECTOR FIELDS IN ALMOST CONTACT MANIFOLDS

作　　者：陈小民[1] 

机构地区：[1]中国石油大学(北京)理学院,北京102249

出　　处：《数学杂志》2017年第3期558-566,共9页Journal of Mathematics

基　　金：Supported by the Science Foundation of China University of PetroleumBeijing(2462015YQ0604);partially by the Personnel Training and Academic Development Fund(2462015QZDX02)

摘　　要：本文引入了近切触流形(M,φ,ξ,η,g)中φ~*-解析向量场的概念,并研究了其性质.利用近切触流形的性质,证明了切触度量流形中的φ~*-解析向量场v是Killing向量场且φv不是φ*-解析的.特别地,如果近切触流形M是正规的,得到v与ξ平行且模长为常数.另外,证明了3维的切触度量流形不存在非零的φ~*-解析向量场.In this article, we introduce the conception of φ^＊-analytic vector field in almost contact manifold （M,φ,ξ,η,g） and study its properties. Making use of the properties of almost contact manifold, we prove that in a contact metric manifold the φ^＊-analytic vector field v is Killing, and that φv must not beφ^＊-analytic unless zero vector field. Particularly, if M is normal, we get that v is collinear to ξ with constant length, and for the case of three dimensional contact metric manifold it is proved that there does not exist a non-zero φ^＊-analytic vector field.

关 键 词：φ^＊-解析向量场 KILLING向量场 近切触结构 切触度量流形 SASAKI流形 

分 类 号：O186.12[理学—数学]