关于带有Ricci孤子的trans-Sasakian流形的注记(英文)  

REMARKS ON RICCI SOLITONS IN TRANS-SASAKIAN MANIFOLDS

作　　者：陈小民 武国宁 

机构地区：[1]中国石油大学(北京)理学院数学系,北京102249

出　　处：《数学杂志》2014年第4期603-609,共7页Journal of Mathematics

基　　金：supported by the NNSF of China(11071257);Science Foundation of China University of Petroleum,Beijing;supported by Science and Technology Research Projectof Heilongjiang Provincial Department of Education(12511412)

摘　　要：本文主要研究带有Ricci孤子的(α,β)型trans-Sasakian流形,证明了带有Ricci孤子(g,ξ,λ)的3-维紧致trans-Sasakian流形是一个Sasakian流形.此外,如果α,β是常数,得到带有梯度Ricci孤子的trans-Sasakian流形是Einstein流形.In this article we mainly study Ricci solitons in trans-Sasakian manifold of type （α,β）. By the calculation of Ricci tensor, we obtain that 3-dimensional compact trans-Sasakian manifold equipping with Ricci solitons （g, ξ,λ） is homothetic to a Sasakian manifold and a trans- Sasadkian manifold admitting a gradient Ricci soliton is an Einstein manifold in case of α,β are constants.

关 键 词：Ricci孤子 梯度Ricci孤子 trans-Sasakian流形 SASAKIAN流形 EINSTEIN流形 

分 类 号：O186.12[理学—数学]