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G2-structures with parallel skew-symmetric torsion
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DOI：10.1007/s10231-026-01678-0.png)
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Abstract
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We classify 7-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in G(2), up to naturally reductive homogeneous spaces and nearly parallel G(2)-structures. This extends and completes the classification initiated by Th. Friedrich in the cocalibrated case. Incidentally, we also obtain the list of SU(3) geometries with parallel skew-symmetric torsion, up to naturally reductive homogeneous spaces and nearly Kahler manifolds.
Keywords:
Parallel skew-symmetric torsion
G(2)-structures
SU(3)-structures
Sasaki structures
(alpha, delta)-Sasaki structures
Twistor spaces
Journal
A
IF:
0.9
Papers:
75
Citations:
0
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Cited Papers