CLASSES OF CONNECTIONS ASSOCIATED WITH DISTRIBUTIONS ON PRODUCT SPACES

Abstract

It is assumed that an n-dimensional distribution is given on an (n+M)-dimensional product space. The latter is endowed with a connection, by means of which the covariant exterior derivatives of the functions that specify the distribution are defined. It is postulated that the connection be such that these derivatives vanish identically. This gives rise to an analysis of the integrability conditions associated with the distribution in terms of appropriate torsion and curvature 2-forms. A further specialization of the connection leads to Edelen's theory [1] of distributions on spaces of fibres.