Work

On the structure of compact strong HKT manifolds

Year: 2025

Type: preprint

Abstract: We study the geometry of compact strong HKT and, more generally, compact BHE manifolds. We prove that any compact BHE manifold with full holonomy must be Kähler and we establish a similar result for strong HKT manifolds. Additionally, we demonstrate a rigidity theorem for strong HKT structures on solvmanifolds and we completely classify those with parallel Bismut torsion. Finally, we introduce the Ricci foliation for hypercomplex manifolds and analyze its properties for compact, simply connected, 8-dimensional strong HKT manifolds, proving that they are always Hopf fibrations over a compact $4$-dimensional orbifold.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.06058

Authors: Brienza, Beatrice, Fino, Anna, Grantcharov, Gueo, Verbitsky, Misha

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6910779728

Cites:

Cited by:

Related to: