Geodesic
Bol three-webs $B_m^{\triangledown}$ with torsion tensor of rank $\rho$
Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1164-1210

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The infinitesimal properties of multidimensional Bol three-webs with covariantly constant curvature tensor (webs $B_m^{\triangledown}$) are considered, and a foundation for classifying such webs in accordance with the rank of the torsion tensor is laid. For a three-web $B_m^{\triangledown}$ of rank $\rho$ Cartan's method is used to construct an adapted frame and find the corresponding system of (differential) structure equations. A three-web $B_m^{\triangledown}$ of rank $\rho$ is shown to have a normal subweb that is a group web; the corresponding factor web is a regular three-web. By integrating the structure equations new families of examples of multidimensional three-webs of special form and smooth Bol loops are discovered which are generalizations of a semidirect product of two Abelian Lie groups. Bibliography: 40 titles.
Keywords: multidimensional three-web, Bol three-web, elastic three-web, $G$-web, smooth Bol loop. 
@article{SM_2018_209_8_a3,
     author = {E. A. Onoprienko and A. M. Shelekhov},
     title = {Bol three-webs $B_m^{\triangledown}$ with torsion tensor of rank $\rho$},
     journal = {Sbornik. Mathematics},
     pages = {1164--1210},
     publisher = {mathdoc},
     volume = {209},
     number = {8},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_8_a3/}
}
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E. A. Onoprienko; A. M. Shelekhov. Bol three-webs $B_m^{\triangledown}$ with torsion tensor of rank $\rho$. Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1164-1210. http://geodesic.mathdoc.fr/item/SM_2018_209_8_a3/