On Connections Of Cartan

Abstract

Introduction. Consider a differentiable manifold M and the tangent bundle T(M) over M , the structure group of which is usually the general linear group G '. Let P ' be the principal fibre bundle associated with T(M). Consider the fibre F of T(M) as an affine space, then we have acting on F the affine transformation group G , which contains G ' as the isotropic subgroup.