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On canonical reductants of spaces of constant curvature. (Russian) Zbl 0568.53027
Webs and quasigroups, Collect. sci. Works, Kalinin 1984, 76-83 (1984).
[For the entire collection see Zbl 0538.00007.]
In his previous notes [Mat. Zametki 12, 605-616 (1972; Zbl 0258.20066) and Dokl. Akad. Nauk SSSR 205, 533-536 (1972; Zbl 0291.18006)] the first author constructed the notion of quasireductant and reductant of a homogeneous space. In this paper the authors study the canonical reductant of the homogeneous space \(SO(n+1)/S(O(n)\times O(1))\) of constant curvature obtaining a matrix model of such a reductant. Next, they obtain a necessary condition for a given smooth loop to be the canonical symmetric loop of a space of constant curvature.
Reviewer: V.Oproiu

53C30 Differential geometry of homogeneous manifolds
22E05 Local Lie groups