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arXiv · 1104.2085

Holonomy of the Obata connection on SU(3)

Andrey Soldatenkov
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Abstract

A hypercomplex structure on a smooth manifold is a triple of integrable almost complex structures satisfying quaternionic relations. The Obata connection is the unique torsion-free connection that preserves each of the complex structures. The holonomy group of the Obata connection is contained in $GL(n, \mathbb{H})$. There is a well-known construction of hypercomplex structures on Lie groups due to Joyce. In this paper we show that the holonomy of the Obata connection on SU(3) coincides with $GL(2, \mathbb{H})$.

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Andrey Soldatenkov. 2011-07-15. Holonomy of the Obata connection on SU(3). https://doi.org/10.1093/imrn%2Frnr152

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