Title: Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity
Authors: A.A. Agrachev, A.V. Sarychev
Journal title: Control, Optimisation, and Calculus of Variations
Year: 1999
Volume: 4
Pages: 377-403
Abstract:

We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlin´eaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating and medium fat) such that the corresponding sub-Riemannian metrics are subanalytic. To characterize these classes of distributions we determine the dimensions of the manifolds on
which generic germs of distributions of given rank are respectively 2-generating or medium fat.