On products of locally conformally K\"ahler manifolds

Miron Stanciu

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arXiv · 2609.05964

On products of locally conformally K\"ahler manifolds

Miron Stanciu

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Abstract

We prove that no product of positive-dimensional compact complex manifolds admits a strict locally conformally K\"ahler (lcK) metric. This solves a long-standing conjecture in lcK geometry, previously established only under certain conditions.

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Miron Stanciu. 2026-09-05. On products of locally conformally K\"ahler manifolds. https://arxiv.org/abs/2609.05964

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