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subriemannian geometry

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Subriemannian geodesics of Carnot groups of step 3 ∗
Kanghai Tan, Xiaoping Yang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 1 / January 2013

Published online by Cambridge University Press:

12 June 2012, pp. 274-287

Print publication:

January 2013
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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.