The Stability of Generalized Ricci Solitons

Abstract In Garcia-Fernandez and Streets (Generalized Ricci flow, volume 76 of university lecture series, American Mathematical Society, Providence, 2021) Oliynyk et al. (Nucl Phys B 739(3):441–458, 2006), it was shown that the generalized flow is gradient a functional $$\lambda $$ λ generalizing Perelman’s for flow. this work, we further computed second variation formula proved Bismut-flat, Einstein manifold linearly stable under some curvature assumptions. last part paper, I dynamical stability linear are equivalent on steady soliton ( g , H f ). This generalizes results in Haslhofer Müller (Math Ann 360(1–2):547–553, 2014), Kröncke (Stability Manifolds, 2014, Commun Anal Geom 28(2):351–394, 2020), Raffero Vezzoni (On behaviour 2020) Sesum (Duke Math J 133(1):1–26, 2006).