Geometries with parallel, skew-symmetric and closed torsion

Andrei Moroianu; Paul Schwahn

Geometries with parallel, skew-symmetric and closed torsion

Differential Geometry 2026-05-14 v1

Authors: Andrei Moroianu , Paul Schwahn

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.

Keywords

Riemannian manifolds metric connection parallel torsion skew-symmetric torsion closed torsion PSCT manifolds G-structures almost Hermitian structures Gray-Hervella classes

Cite

@article{arxiv.2605.13227,
  title  = {Geometries with parallel, skew-symmetric and closed torsion},
  author = {Andrei Moroianu and Paul Schwahn},
  journal= {arXiv preprint arXiv:2605.13227},
  year   = {2026}
}

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27 pages

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