Holonomy of the Obata connection on SU(3)

Details Holonomy of the Obata connection on SU(3) Holonomy of the Obata connection on SU(3)

2011-04-11

arxiv.org/abs/1104.2085v2

Mathematics

Differential Geometry

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

Scientific paper

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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