SubRiemannian geodesics for Carnot groups of step 3

Details SubRiemannian geodesics for Carnot groups of step 3 SubRiemannian geodesics for Carnot groups of step 3

2011-05-04

arxiv.org/abs/1105.0844v2

Mathematics

Differential Geometry

15 pages preprint. to appear on ESAIM: COCV. Some errors are corrected according to the referee's suggestion

Scientific paper

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.

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