An Almost Complex Chern–Ricci Flow

Tao Zheng

doi:10.1007/s12220-017-9898-9

An Almost Complex Chern–Ricci Flow

Tao Zheng^*

^*此作品的通讯作者

Université Grenoble Alpes

科研成果: 期刊稿件 › 文章 › 同行评审

32 引用（Scopus）

摘要

We consider the evolution of an almost Hermitian metric by the (1, 1) part of its Chern–Ricci form on almost complex manifolds. This is an evolution equation first studied by Chu and coincides with the Chern–Ricci flow if the complex structure is integrable and with the Kähler–Ricci flow if moreover the initial metric is Kähler. We find the maximal existence time for the flow in term of the initial data and also give some convergence results. As an example, we study this flow on the (locally) homogeneous manifolds in more detail.

源语言	英语
页（从-至）	2129-2165
页数	37
期刊	Journal of Geometric Analysis
卷	28
期	3
DOI	https://doi.org/10.1007/s12220-017-9898-9
出版状态	已出版 - 1 7月 2018
已对外发布	是

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Zheng, T. (2018). An Almost Complex Chern–Ricci Flow. Journal of Geometric Analysis, 28(3), 2129-2165. https://doi.org/10.1007/s12220-017-9898-9

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AB - We consider the evolution of an almost Hermitian metric by the (1, 1) part of its Chern–Ricci form on almost complex manifolds. This is an evolution equation first studied by Chu and coincides with the Chern–Ricci flow if the complex structure is integrable and with the Kähler–Ricci flow if moreover the initial metric is Kähler. We find the maximal existence time for the flow in term of the initial data and also give some convergence results. As an example, we study this flow on the (locally) homogeneous manifolds in more detail.

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An Almost Complex Chern–Ricci Flow

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