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中文摘要：
拟爱因斯坦度量是Ricci孤立子的一般形式.如果流形非紧,关于闭流形上拟爱因斯坦度量的势函数估计还没有结果.文章应用关于数量曲率估计的结果得到了完备非紧黎曼流形上关于拟爱因斯坦度量势函数的下界估计,并给出一个拟爱因斯坦度量的例子.
英文摘要：
The quasi-Einstein metric is the general form of the Ricci soliton. The estimates of the scalar curvatures and the potential function for quasi-Einstein metrics on closed manifolds have been researched by many scholars. But there is no result about the estimate of the potential function when the manifold is noncompact. In this paper, lower bound estimates of the potential function for quasi-Einstein metrics on complete noncompact have been obtained in Riemannian manifolds by using the estimate of the scalar curvature, and an example of the quasi-Einstein metrich has also been given.
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