中文摘要：

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.

英文摘要：

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.