近Ricci孤立子的刚性

通过计算无迹曲率张量模长平方的X-Laplace算子, 讨论近Ricci孤立子的刚性. 在数量曲率非负的假设下, 证明完备近Ricci孤立子在逐点拼挤条件下等距于Rⁿ或Sⁿ的有限商. 对紧致近Ricci孤立子, 在数量曲率为正的假设下, 给出一个积分不等式, 并证明等号成立当且仅当孤立子等距于Sⁿ的有限商.

Rigidity of Almost Ricci Solitons

We discussed the rigidity of almost Ricci solitons by calculating the X-Laplacian for the module square of the trace-free curvature tensor. Under the assumption that the scalar curvature was nonnegative, we proved that a complete almost Ricci solitons were isometric to a finite quotient of Rⁿ or Sⁿ under a pointwise pinching condition. For a compact almost Ricci soliton, we gave an integral inequality and proved that the equal sign held if and only if the soliton was isometric to a finite quotient of Sⁿ under the assumption that the scalar curvature was positive.