Holonomy of the Obata connection on SU(3)

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 $GL(2,\mathbb{H})$.

v.2.0, 17 pages, minor corrections, 2 references added

References in corpus (1)

• Geometry of Hyper-Kähler Connections with Torsion

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