An Almost Complex Chern–Ricci Flow

Tao Zheng

doi:10.1007/s12220-017-9898-9

An Almost Complex Chern–Ricci Flow

Tao Zheng^*

^*Corresponding author for this work

Université Grenoble Alpes

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2129-2165
Number of pages	37
Journal	Journal of Geometric Analysis
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s12220-017-9898-9
Publication status	Published - 1 Jul 2018
Externally published	Yes

Keywords

Almost Hermitian metric
Evolution equation
Maximal time existence
The Chern–Ricci form

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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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KW - Evolution equation

KW - Maximal time existence

KW - The Chern–Ricci form

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An Almost Complex Chern–Ricci Flow

Abstract

Keywords

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