On pseudoholomorphic map between almost Hermitian manifolds

Chiakuei Peng; Xiaowei Xu

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arXiv · 2105.09607

On pseudoholomorphic map between almost Hermitian manifolds

Chiakuei Peng·Xiaowei Xu

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Abstract

In this paper, we use the canonical connection instead of Levi-Civita connection to study the smooth maps between almost Hermitian manifolds, especially, the pseudoholomorphic ones. By using the Bochner formulas, we obtian the $C^2$-estimate of canonical second fundamental form, Liouville type theorems of pseudoholomorphic maps, pseudoholomorphicity of pluriharmonic maps, and Simons integral inequality of pseudoholomorphic isometric immersion.

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Chiakuei Peng, Xiaowei Xu. 2021-05-20. On pseudoholomorphic map between almost Hermitian manifolds. https://arxiv.org/abs/2105.09607

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