保持Ricci孤立子结构的共形变换

Conformal Transformations to Keep the Structure of a Ricci Soliton

研究了保持Ricci孤立子结构的共形变换,证明了2维梯度Ricci孤立子的共形刚性定理,给出了保持梯度Ricci孤立子结构的共形变换在维数大于2的情况下必须满足的条件.

In this paper,we study the conformal transformations which preserve the gradient Ricci solitons structure,and then obtain conformal rigidity theorems on 2-dimensional gradient Ricci solitons.Moreover,we give a necessary condition for conformal transformation of preserving the Ricci Soliton Structure for higher dimension.