Geometries with parallel, skew-symmetric and closed torsion

Andrei Moroianu; Paul Schwahn

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arXiv · 2605.13227

Geometries with parallel, skew-symmetric and closed torsion

Andrei Moroianu·Paul Schwahn

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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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Andrei Moroianu, Paul Schwahn. 2026-05-13. Geometries with parallel, skew-symmetric and closed torsion. https://arxiv.org/abs/2605.13227

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