Displaying similar documents to “Sub-riemannian metrics : minimality of abnormal geodesics versus subanalyticity”

Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity

Andrei A. Agrachev, Andrei V. Sarychev (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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. , p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating and medium...

Hierarchy of integrable geodesic flows.

Peter Topalov (2000)

Publicacions Matemàtiques

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A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.