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Geometries with parallel, skew-symmetric and closed torsion

· 2026 · math.DG · arXiv 2605.13227

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abstract

We study Riemannian manifolds carrying a metric connection with parallel, skew-symmetric and closed torsion, which we call in short PSCT manifolds. We prove that PSCT manifolds always locally split into a product of well-understood factors, allowing a complete local classification. Further, we investigate various $G$-structures of PSCT type, with a focus on almost Hermitian structures and their possible Gray--Hervella classes.

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2026 1

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Semi-integrable almost hyperhermitian structures

math.DG · 2026-06-21 · unverdicted · novelty 5.0

Introduces semi-integrable almost hyperhermitian structures, partitions them into four non-empty classes, and constructs examples on reductive compact-type Lie algebras of dimension 4n (n≥2).

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  • Semi-integrable almost hyperhermitian structures math.DG · 2026-06-21 · unverdicted · none · ref 22 · internal anchor

    Introduces semi-integrable almost hyperhermitian structures, partitions them into four non-empty classes, and constructs examples on reductive compact-type Lie algebras of dimension 4n (n≥2).