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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniqueness of torsion free connection on some invariant structures on Lie groups


Authors: Michel Nguiffo Boyom and Georges Giraud
Journal: Trans. Amer. Math. Soc. 280 (1983), 797-808
MSC: Primary 53C05
MathSciNet review: 716851
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Abstract: Let $ \mathcal{G}$ be a connected Lie group with Lie algebra $ \mathfrak{g}$. Let $ \operatorname{Int}(\mathfrak{g})$ be the group of inner automorphisms of $ \mathfrak{g}$. The group $ \mathcal{G}$ is naturally equipped with $ \operatorname{Int}(\mathfrak{g})$-reductions of the bundle of linear frames on $ \mathcal{G}$. We investigate for what kind of Lie group the 0-connection of E. Cartan is the unique torsion free connection adapted to any of those $ \operatorname{Int}(\mathfrak{g})$-reductions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0716851-4
PII: S 0002-9947(1983)0716851-4
Keywords: $ G$-structure, torsion free connection, prolongation, symmetric operator of Lie algebra
Article copyright: © Copyright 1983 American Mathematical Society