${\mathrm G}_2$-structures with parallel skew-symmetric torsion
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908940370968576 |
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| author | Moroianu, Andrei Semmelmann, Uwe |
| author_facet | Moroianu, Andrei Semmelmann, Uwe |
| contents | We classify $7$-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in $\mathrm{G}_2$, up to naturally reductive homogeneous spaces and nearly parallel $\mathrm{G}_2$-structures. This extends and completes the classification initiated by Th. Friedrich in the cocalibrated case. Incidentally, we also obtain the list of $\mathrm{SU}(3)$ geometries with parallel skew-symmetric torsion, up to naturally reductive homogeneous spaces and nearly Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ${\mathrm G}_2$-structures with parallel skew-symmetric torsion Moroianu, Andrei Semmelmann, Uwe Differential Geometry We classify $7$-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in $\mathrm{G}_2$, up to naturally reductive homogeneous spaces and nearly parallel $\mathrm{G}_2$-structures. This extends and completes the classification initiated by Th. Friedrich in the cocalibrated case. Incidentally, we also obtain the list of $\mathrm{SU}(3)$ geometries with parallel skew-symmetric torsion, up to naturally reductive homogeneous spaces and nearly Kähler manifolds. |
| title | ${\mathrm G}_2$-structures with parallel skew-symmetric torsion |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.02899 |