Rigidity of complete generic shrinking Ricci solitons

摘要

AbstractLet(Mn,g,X)be a complete generic shrinking Ricci soliton of dimensionn≥3. In this paper, by employing curvature inequalities, the formula ofX-Laplacian for the norm square of the trace-free curvature tensor, the weak maximum principle and the estimate of the scalar curvature of(Mn,g), we prove some rigidity results for(Mn,g,X). In particular, it is showed that(Mn,g,X)is isometric toRnor a finite quotient ofSnunder a pointwise pinching condition. Moreover, we establish several optimal inequalities and classify those shrinking solitons for equalities.]]>