Geodesic
Subriemannian geodesics of Carnot groups of step 3
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 274-287 Cet article a éte moissonné depuis la source Numdam

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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.

DOI : 10.1051/cocv/2012006
Classification : 53C17, 49K30
Keywords: subriemannian geometry, geodesics, calculus of variations, Goh condition, generalized Legendre-Jacobi condition 
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Tan, Kanghai; Yang, Xiaoping. Subriemannian geodesics of Carnot groups of step 3. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 274-287. doi: 10.1051/cocv/2012006

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