Bol three-webs $B_m^{\triangledown}$ with torsion tensor of rank $\rho$

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.