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PreprintCC0arXiv

HKT geometry on locally conformally hyperkähler manifolds

  • Giovanni Gentili
  • Luigi Vezzoni
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Abstract

We study the HKT geometry of compact locally conformally hyperkähler manifolds. We prove that on these manifolds the quaternionic Monge-Ampère equation is always solvable, extending results of Alesker and of Dinew-Sroka, and we confirm the conjecture on the maximal existence time of the HKT-Ricci flow. On quaternionic Hopf surfaces we construct non-trivial HKT solitons and prove convergence of the normalized flow for symmetric initial data.

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Cite

BibTeXRIS
BibTeX
@misc{gentili2026geometry,
  title = {{HKT geometry on locally conformally hyperkähler manifolds}},
  author = {Giovanni Gentili and Luigi Vezzoni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07897},
  eprint = {2610.07897},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07897},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - HKT geometry on locally conformally hyperkähler manifolds
AU  - Giovanni Gentili
AU  - Luigi Vezzoni
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.07897
UR  - https://arxiv.org/abs/2610.07897
AB  - We study the HKT geometry of compact locally conformally hyperkähler manifolds. We prove that on these manifolds the quaternionic Monge-Ampère equation is always solvable, extending results of Alesker and of Dinew-Sroka, and we confirm the conjecture on the maximal existence time of the HKT-Ricci flow. On quaternionic Hopf surfaces we construct non-trivial HKT solitons and prove convergence of the normalized flow for symmetric initial data.
ER  -