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On types of non-integrable geometries
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abstract
We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a $\Spin(7)$-structure play a special role. Any geometry of that type admits a unique connection with totally skew-symmetric torsion. Under weak conditions on the structure group we prove that this geometry is the only one with this property. Finally, we discuss the automorphism group of a Riemannian manifold with a fixed non-integrable $\mathrm{G}$-structure.
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Dynamics of Cayley Forms
Constructs two-parameter family of torsion-squared Lagrangians for Spin(7)-structures whose field equations are expressed via exterior derivatives, with one case integrating to scalar curvature and reproducing Einstei...
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