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Reductive homogeneous spaces and nonassociative algebras

Alberto Elduque (2020)

Communications in Mathematics

The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.

Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines

Bensalem, Naceurdine (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.

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