A connection theoretic approach to sub-Riemannian geometry

We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnormal extremals will be derived. We also treat the problem of characterizing those curves that verify both the nonholonomic equations and the so-called vakonomic equations for a "free" particle submitted to some kinematical constraints. (C) 2002 Published by Elsevier Science B.V.