Commutator Formulas for Gradient Ricci Shrinkers and Their Application to Linear Stability of Gradient Ricci Shrinkers.

In this paper we have found a number of commutator formulas between the weighted divergence, the weighted Laplacian, the weighted Lichnerowicz Laplacian and the Lie derivtive on closed orientable gradient Ricci shrinkers, then using them we have generalized a Theorem of Cao and Zhu about the necessary condition for linear stability of a gradient Ricci shrinker. Recentlly they have also extended our results. [ABSTRACT FROM AUTHOR]