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On differential geometry of Bol loops. (English. Russian original) Zbl 0587.53021
Sov. Math., Dokl. 31, 389-391 (1985); translation from Dokl. Akad. Nauk SSSR 281, 1055-1057 (1985).
The authors show that a local analytic Bol loop is a geodesic loop of an affinely connected space where the affine connection is a curvature-free Cartan connection given on a Lie group. This result allows the authors to use techniques of differential geometry to prove the main structure theorems of the theory of analytical Bol loops [see the recently published book by the authors, Theory of smooth Bol loops (Moscow, 1985; Zbl 0584.53001)].
Reviewer: V.V.Goldberg

MSC:
53A60 Differential geometry of webs
53C35 Differential geometry of symmetric spaces
20N05 Loops, quasigroups
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