近切触流形的φ∗-解析向量场

摘要

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 theφ?-analytic vector field v is Killing, and that φv must not be φ?-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-zeroφ?-analytic vector field.%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.