Geodesic
On one class of Bol three-webs
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Tome 179 (2020), pp. 37-40.

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In this paper, we consider infinitesimal properties of multidimensional mean Bol three-webs with a covariantly constant curvature tensor (webs $B_m^{\triangledown}$) and lay the foundations for classifying such webs by the rank of the torsion tensor. For three-webs $B_m^{\triangledown}$ of rank $\rho$, we construct an adapted frame by the Cartan method and find the corresponding system of structural (differential) equations. We prove that a three-web $B_m^{\triangledown}$ of rank $\rho$ carries a normal subweb, which is a group web, and the corresponding factor-web is a regular three-web. By integrating the structure equations, we find new families of examples of multidimensional three-webs of a special type and smooth Bol loops, which are a generalization of the semidirect product of two Abelian Lie groups.
Keywords: multidimensional three-web, Bol three-web, group three-web, elastic three-web, $G$-web, smooth Bol loop. 
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     title = {On one class of {Bol} three-webs},
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E. A. Onoprienko. On one class of Bol three-webs. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Tome 179 (2020), pp. 37-40. http://geodesic.mathdoc.fr/item/INTO_2020_179_a5/

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