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arXiv · 2510.02899

${\mathrm G}_2$-structures with parallel skew-symmetric torsion

Andrei Moroianu·Uwe Semmelmann
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Abstract

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 K\"ahler manifolds.

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Andrei Moroianu, Uwe Semmelmann. 2025-10-03. ${\mathrm G}_2$-structures with parallel skew-symmetric torsion. https://doi.org/10.1007/s10231-026-01678-0

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