The Stability of Generalized Ricci Solitons

Abstract

In this paper, I computed the second variation formula of the generalized Einstein-Hilbert functional and prove that a Bismut-flat, Einstein manifold is linearly stable under some curvature assumption. In the last part of the paper, I prove that dynamical stability and linear stability are equivalent on a steady gradient generalized Ricci soliton $(g, H,f)$ which generalizes the result done by Kr\"oncke, Haslhofer, Sesum, Raffero, and Vezzoni.