Bol three-webs with covariantly constant curvature tensor

Abstract

We find complete systemof tensor relations characterizing the class ofmultidimensional middle Bol three-webs with covariantly constant curvature tensor, and ascertain the algebraic sense of these relations. We prove the existence of such webs and lay the foundation of their classification in terms of torsion tensor rank. We also show that 6-dimensional non-group webs of such type are the known flexible webs E1 and E2.