|
| 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. |
| 关键词: Ricci孤子 梯度Ricci孤子 trans-Sasakian流形 Sasakian流形 Einstein流形 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:Partially supported by the NNSF of China (11071257);Science Foundation of China University of Petroleum,Beijing;Partially supported by Science and Technology Research Project of Heilongjiang Provincial Department of Education (12511412). |
|
| REMARKS ON RICCI SOLITONS IN TRANS-SASAKIAN MANIFOLDS |
|
CHEN Xiao-min,WU Guo-ning
|
| Abstract: |
| 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 transSasadkian manifold admitting a gradient Ricci soliton is an Einstein manifold in case of α,β are constants. |
| Key words: Ricci soliton gradient Ricci soliton trans-Sasakian manifold Sasakian manifold Einstein manifold |
