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

Abstract

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 whose 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.