On one class of three-webs with covariantly constant curvature and torsion tensors

A special class of multidimensional three-webs $W^\nabla$ with covariantly constant curvature and torsion tensors is considered, the curvature tensor having the minimal rank. It is proved that there is a subfamily of adapted frames of the web $W^\nabla$ whose torsion tensor components are constant and the curvature tensor has a unique nonzero component. The structure equations of the webs of this class are found and some of their properties are described.