| 摘要: |
| 本文引入了近切触流形（M，ø，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. |
| 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 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:Supported by the Science Foundation of China University of PetroleumBeijing (2462015YQ0604) and partially by the Personnel Training and Academic Development Fund (2462015QZDX02). |
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| φ*-ANALYTIC VECTOR FLELDS IN ALMOST CONTACT MANIFOLDS |
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CHEN Xiao-min
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College of Science, China University of Petroleum-Beijing, Beijing 102249, China
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| Abstract: |
| In this article, we introduce the conception of φ*-analytic vector field in almost contact manifold (M, ø, 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 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-zero φ*-analytic vector field. |
| Key words: φ*-analytic vector field Killing vector field almost contact structure contact manifold Sasakian manifold |
