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ArticleOriginal scientific text

Title

Abnormality of trajectory in sub-Riemannian structure

Authors 1, 1

Affiliations

  1. LAMA, Université de Savoie, Campus Scientifique, 73376 Le Bourget du Lac Cedex, France

Abstract

In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, C1-rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not C1-rigid and which can be minimizing or non minimizing according to different metrics.

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Banach Center Publications
1995/32/1
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Pages:
301-317
Main language of publication
English
Published
1995
Exact and natural sciences