An Integrability Condition for Simple Lie Groups II
Copyright policy )An Integrability Condition for Simple Lie Groups II
It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ 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].
- McMaster University Canada
Mathematics - Differential Geometry, simple Lie groups and algebras, Differential geometry of homogeneous manifolds, \(G\)-structure, Differential Geometry (math.DG), FOS: Mathematics, \(G\)-structures
Mathematics - Differential Geometry, simple Lie groups and algebras, Differential geometry of homogeneous manifolds, \(G\)-structure, Differential Geometry (math.DG), FOS: Mathematics, \(G\)-structures
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