Volume 19, Number 1, January-March 2013
|Page(s)||274 - 287|
|Published online||12 June 2012|
Subriemannian geodesics of Carnot groups of step 3∗
Department of Applied Mathematics, Nanjing University of Science
& Technology, Nanjing
2 School of Science, Nanjing University of Science & Technology, Nanjing 210094, P.R. China
Revised: 2 November 2011
In Carnot groups of step ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.
Mathematics Subject Classification: 53C17 / 49K30
Key words: Subriemannian geometry / geodesics / calculus of variations / Goh condition / generalized Legendre-Jacobi condition
© EDP Sciences, SMAI, 2012
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