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 Kröncke, Haslhofer, Sesum, Raffero, and Vezzoni.

References in corpus (7)

• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• Stability and instability of Ricci solitons
• Dynamical stability and instability of Ricci-flat metrics
• Stability of Einstein metrics under Ricci flow
• On the stability of Einstein manifolds
• The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics
• On the dynamical behaviour of the generalized Ricci flow

Cited by in corpus (5)

• Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries
• Stability and moduli space of generalized Ricci solitons
• The stability of non-Kähler Calabi-Yau metrics
• Differential calculus for generalized geometry and geometric Lax flows
• Generalized Ricci flow on aligned homogeneous spaces