Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Brienza, Beatrice
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223238220