A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle

2. Generalities [2; l]. If xGA, vi, v2(E.Xx, let (vu v2) denote the inner product that defines the Riemannian metric. If a: [0, l]—»A is a curve, let a':t-^a'(t) denote the tangent vector field to a. If v: H»(i)GI,(i) is a vector-field along a, let Av denote the covariant derivative of v along a [l]. Let us recall how it is defined by Elie Cartan's method of orthonormal moving frames: Suppose U is an open set of A and w, (léi,j, k • ■ • 5¡w = dim X, summation convention) 1-differential forms in U with