Analog of selfduality in dimension nine

Details Analog of selfduality in dimension nine Analog of selfduality in dimension nine

2011-09-04

arxiv.org/abs/1109.0757v2

Mathematics

Differential Geometry

43 pages. We added a suggestion of Robert Bryant

Scientific paper

We introduce a type of Riemannian geometry in nine dimensions, which can be viewed as the counterpart of selfduality in four dimensions. This geometry is related to a 9-dimensional irreducible representation of ${\bf SO}(3) \times {\bf SO} (3)$ and it turns out to be defined by a differential 4-form. Structures admitting a metric connection with totally antisymmetric torsion and preserving the 4-form are studied in detail, producing locally homogeneous examples which can be viewed as analogs of self-dual 4-manifolds in dimension nine.

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