本项目拟研究具有特殊几何结构的黎曼流形，即把Ricci Soliton方程与Static空间方程统一起来研究，主要研究内容如下：1）研究具有此结构的紧致黎曼流形，在一定的条件下，得到刚性结果；2）研究具有此结构的完备黎曼流形，研究位势函数的增长行为；3）研究具有此结构的Kahler流形，给出分类；4）研究具有此结构的子流形，给出几何刻画。

The purpose of this project is to study the Riemannian manifolds with special geometrical structures. That is, we treat the Ricci soliton and the static equation in an unified way. Main concents of this project is the following: 1) Under some assumptions, we study some rigidity results for compact Riemannian manifolds with such geometrical structures; 2) We study growth rate for complete Riemannian manifolds with such geometrical structures; 3) Classifications of Kahler manifolds with such geometrical structures will be given; 4) We also study submanifolds with such geometrical structures and give classifications on geometry.