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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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Cite

BibTeXRIS
BibTeX
@misc{moroianu2026geometries,
  title = {{Geometries with parallel, skew-symmetric and closed torsion}},
  author = {Andrei Moroianu and Paul Schwahn},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2605.13227},
  eprint = {2605.13227},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.13227},
}
RIS
TY  - UNPB
TI  - Geometries with parallel, skew-symmetric and closed torsion
AU  - Andrei Moroianu
AU  - Paul Schwahn
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2605.13227
UR  - https://arxiv.org/abs/2605.13227
AB  - 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.
ER  -