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arXiv · 2408.09648

Rigidity results for non-K\"ahler Calabi-Yau geometries on threefolds

Vestislav Apostolov·Giuseppe Barbaro·Kuan-Hui Lee·Jeffrey Streets
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Abstract

We derive a canonical symmetry reduction associated to a compact non-K\"ahler Bismut-Hermitian-Einstein manifold. In real dimension $6$, the transverse geometry is conformally K\"ahler, and we give a complete description in terms of a single scalar PDE for the underlying K\"ahler structure. In the case when the soliton potential is constant, we show that that the Bott-Chern number $h^{1,1}_{BC} \geq 2$, and that equality holds if and only if the metric is Bismut-flat, and hence a quotient of either $\SU(2) \times \mathbb R \times \mathbb C$ or $\SU(2) \times \SU(2)$.

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Vestislav Apostolov, Giuseppe Barbaro, Kuan-Hui Lee, Jeffrey Streets. 2024-08-19. Rigidity results for non-K\"ahler Calabi-Yau geometries on threefolds. https://arxiv.org/abs/2408.09648

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