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Subriemannian geodesics of Carnot groups of step 3∗

Published online by Cambridge University Press:  12 June 2012

Kanghai Tan  and
Xiaoping Yang
Kanghai Tan
Affiliation:
Department of Applied Mathematics, Nanjing University of Science & Technology, Nanjing 210094, P.R. China. khtan@mail.njust.edu.cn
Xiaoping Yang
Affiliation:
School of Science, Nanjing University of Science & Technology, Nanjing 210094, P.R. China; yangxp@mail.njust.edu.cn
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Abstract

In Carnot groups of step  ≤ 3, all subriemannian geodesics are proved to be normal. Theproof is based on a reduction argument and the Goh condition for minimality of singularcurves. The Goh condition is deduced from a reformulation and a calculus of the end-pointmapping which boils down to the graded structures of Carnot groups.

Keywords

Subriemannian geometrygeodesicscalculus of variationsGoh conditiongeneralized Legendre-Jacobi condition
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 274 - 287
Copyright
© EDP Sciences, SMAI, 2012

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