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arXiv · 2609.08238

Orthogonal complex structures on flat tori

Qingsong Wang·Shing-Tung Yau·Fangyang Zheng
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Abstract

We classify compact Hermitian manifolds with flat Levi-Civita connection. This is equivalent to the classification of all orthogonal complex structures on flat tori. It generalized the work of Khan, Yang, and Zheng in 2017 where they solved the case in complex dimension three.

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Qingsong Wang, Shing-Tung Yau, Fangyang Zheng. 2026-09-08. Orthogonal complex structures on flat tori. https://arxiv.org/abs/2609.08238

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