Convergence of the Hesse-Koszul flow on compact Hessian manifolds

Stéphane Puechmorel (1) , Tat Dat Tô (1)

1 ENAC - Ecole Nationale de l'Aviation Civile

We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delano\"e and Caffarelli-Viaclovsky.

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]

Stéphane Puechmorel, Tat Dat Tô. Convergence of the Hesse-Koszul flow on compact Hessian manifolds. 2020. ⟨hal-02434378⟩