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 nonlinéaire 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.

Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity / Agrachev, Andrey; Sarychev, A.. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 4:(1999), pp. 377-403. [10.1051/cocv:1999114]

Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity

Agrachev, Andrey;
1999-01-01

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 nonlinéaire 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.
1999
4
377
403
https://doi.org/10.1051/cocv:1999114
Agrachev, Andrey; Sarychev, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/16991
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