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arXiv · 2610.30130

Generalized Kahler BHE threefolds

Beatrice Brienza
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Abstract

We study the notion of generalized Kahler Bismut--Hermitian--Einstein (GKBHE) manifolds, namely generalized Kähler manifolds for which both Bismut Ricci forms vanish, and we develop a theory for such structures on compact threefolds. We organize the analysis according to the horizontal rank, an invariant taking values in $\{0,1,2\}$ that measures the relative position of the canonical foliations associated with the two Hermitian structures. We characterize the case of horizontal rank $0$ (which corresponds to Kähler Ricci flat geometry) and describe the case of horizontal rank $1$, revealing its close interplay with the steady $ν$-soliton equation in Kähler geometry. This description also provides a tool for constructing new compact GKBHE threefolds.

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Beatrice Brienza. 2026-10-21. Generalized Kahler BHE threefolds. https://arxiv.org/abs/2610.30130

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