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arXiv · 2610.06067

A Complex Structure on $T^2\times S^4$: The Genus-One Case of Calabi's Problem

Min Gao·Zizhou Tang·Wenjiao Yan
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Abstract

We construct a complex structure on $T^2\times S^4$, giving an affirmative answer to the genus-one case of Calabi's problem. The resulting compact complex threefold is non-Kähler and admits no biholomorphic product decomposition.

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Min Gao, Zizhou Tang, Wenjiao Yan. 2026-10-05. A Complex Structure on $T^2\times S^4$: The Genus-One Case of Calabi's Problem. https://arxiv.org/abs/2610.06067

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