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Differential geometry of Cartan connections. (English) Zbl 0857.53011

The authors introduce and study a generalized Cartan connection as a deformation of a local Lie group structure on a manifold, i.e., a 1-form \(\lambda\) with values in a Lie algebra \(\eta\) which is nondegenerate and satisfies the Maurer-Cartan equation. They prove that many notions and results of the differential geometry of group manifolds survive and are still valid in this more general setting.

MSC:

53B05 Linear and affine connections
53C10 \(G\)-structures
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