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arXiv · 1109.0757

Analog of selfduality in dimension nine

Anna Fino·Pawel Nurowski
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Abstract

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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Anna Fino, Pawel Nurowski. 2011-09-13. Analog of selfduality in dimension nine. https://arxiv.org/abs/1109.0757

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