On types of non-integrable geometries

Details On types of non-integrable geometries On types of non-integrable geometries

2002-05-14

arxiv.org/abs/math/0205149v1

Mathematics

Differential Geometry

Latex2.09, 12 pages

Scientific paper

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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