GENERALIZED AFFINE DEVELOPMENTS

Abstract

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve xt (t ∈ [0, 1]) in M into the affine tangent space at x0 (∈ M ) with respect to a given generalized affine connection in the bundle of affine frames over M .

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