Commutator formulas for gradient Ricci shrinker and their application to linear stability

Abstract

In this paper we have found some commutator formulas between $di{v}_f,{\Delta }_{f,L},di{v}_f^{†},{\Delta }_f$ on closed orientable $GR{S}^{+}$ metrics (Gradient Ricci Shrinker), then with them we have generalized a Theorem of Cao and Zhu about necessary condition for linear stability of a $GR{S}^{+}$.

References in corpus (4)

• Gaussian densities and stability for some Ricci solitons
• Stability and instability of Ricci solitons
• On a classification of the gradient shrinking solitons
• Stability of non compact steady and expanding gradient Ricci solitons