Convergence of the Hesse–Koszul flow on compact Hessian manifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-16 DOI:10.4171/aihpc/68

Stéphane Puechmorel, Tat Dat Tô

引用次数: 4

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.

查看原文本刊更多论文

紧致Hessian流形上Hesse-Koszul流的收敛性

研究了紧化Hessian流形上hessia - koszul流的长时间特性。当第一个仿射陈氏类为负时，我们证明了流收敛于唯一的黑塞-爱因斯坦度量。我们还得到了任意紧化Hessian流形上的扭曲hessia - koszul流的收敛性结果。这些结果给出了Cheng-Yau和Caffarelli-Viaclovsky给出的唯一黑塞-爱因斯坦度量存在性的替代证明，以及Cheng-Yau、Delano\e和Caffarelli-Viaclovsky给出的真实卡拉比定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.