Convergence of the Hesse-Koszul flow on compact Hessian manifolds

Abstract : 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.
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https://hal-enac.archives-ouvertes.fr/hal-02434378
Contributor : Tat Dat Tô <>
Submitted on : Friday, January 10, 2020 - 8:50:11 AM
Last modification on : Monday, January 13, 2020 - 1:11:55 AM

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  • HAL Id : hal-02434378, version 1
  • ARXIV : 2001.02940

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

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