An Integrability Condition for Simple Lie Groups

Abstract

It is shown that a simple Lie group G (6 SL2) can be locally characterised by an integrability condition on an Aut(g) structure on the tangent bundle, where Aut(g) is the automorphism group of the Lie algebra of G. The integrability condition is the vanishing of a torsion tensor of type (1;2). This is a slight improvement of an earlier result proved in (Min-Oo M., Ruh E.A., in Differential Geometry and Complex Analysis, Springer, Berlin, 1985, 205{211).