On one class of Bol three-webs

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.