Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
Notes on the octonions
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This is an expository paper. Its purpose is to explain the linear algebra that underlies Donaldson-Thomas theory and the geometry of Riemannian manifolds with holonomy in $G_2$ and ${\rm Spin}(7)$.
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UNVERDICTED 3representative citing papers
Computes the right spectrum of the canonical G2-equivariant operator h, yielding slice-independent quartic curves and circles via SU(3) block decomposition after fixing complex slices in O.
A gluing theorem for ACyl associative submanifolds produces closed rigid associatives in twisted connected sum G2-manifolds with topologies S^3, RP^3 and RP^3#RP^3.
citing papers explorer
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On the rigidity of special and exceptional geometries with torsion a closed $3$-form
Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
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Octonionic structure operator and its right spectrum
Computes the right spectrum of the canonical G2-equivariant operator h, yielding slice-independent quartic curves and circles via SU(3) block decomposition after fixing complex slices in O.
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Associative submanifolds in twisted connected sum $G_2$-manifolds
A gluing theorem for ACyl associative submanifolds produces closed rigid associatives in twisted connected sum G2-manifolds with topologies S^3, RP^3 and RP^3#RP^3.