| Issue |
ESAIM: COCV
Volume 19, Number 1, January-March 2013
|
|
|---|---|---|
| Page(s) | 274 - 287 | |
| DOI | https://doi.org/10.1051/cocv/2012006 | |
| Published online | 12 June 2012 | |
Subriemannian geodesics of Carnot groups of step 3∗
1
Department of Applied Mathematics, Nanjing University of Science
& Technology, Nanjing
210094, P.R.
China
khtan@mail.njust.edu.cn
2
School of Science, Nanjing University of Science &
Technology, Nanjing
210094, P.R.
China
yangxp@mail.njust.edu.cn
Received:
10
May
2011
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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