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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{brienza2026generalized,
  title = {{Generalized Kahler BHE threefolds}},
  author = {Beatrice Brienza},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30130},
  eprint = {2610.30130},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30130},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Kahler BHE threefolds
AU  - Beatrice Brienza
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30130
UR  - https://arxiv.org/abs/2610.30130
AB  - 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.
ER  -