Three-webs

Abstract

Abstract Local differential-geometric properties of three-webs formed on a -dimensional manifold by foliations of codimension , and , respectively, are considered. In particular, three-webs defined by complex analytic functions of complex arguments belong to this class of webs. The structure equations of a three-web in an adapted co-frame (in particular, in a natural co-frame) are deduced; the canonical connection on the manifold of a web is introduced; formulae are obtained to calculate (in a natural co-basis) the components of the first structure tensor of a three-web in terms of the derivatives of the function of this web. Three special classes of three-webs are considered in detail: regular and group three-webs and also three-webs generated by holomorphic functions. Bibliography: 17 titles.