关键词: 近Ricci孤立子, 刚性, X-Laplace算子

Abstract: 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.

Key words: almost Ricci solitons, rigidity, X-Laplacian