Calabi-Yau locally conformally K\"ahler manifolds

Giuseppe Barbaro; Alexandra Otiman

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arXiv · 2509.18364

Calabi-Yau locally conformally K\"ahler manifolds

Giuseppe Barbaro·Alexandra Otiman

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Abstract

We study compact locally conformally K\"ahler (lcK) manifolds which are Calabi--Yau, in the sense that $c_1^{BC}(X)=0$. First of all, we prove that all the known lcK manifolds which are Calabi--Yau are Vaisman. Then we prove that an lcK Chern--Ricci flat metric that is Gauduchon is necessarily Vaisman. Finally, specializing to Calabi--Yau solvmanifolds with left-invariant complex structure, we prove that a left-invariant metric is lcK if and only if it is Vaisman. Therefore, they are finite quotients of the Kodaira manifold.

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BibTeX RIS

Giuseppe Barbaro, Alexandra Otiman. 2025-09-22. Calabi-Yau locally conformally K\"ahler manifolds. https://arxiv.org/abs/2509.18364

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