SubRiemannian geodesics for Carnot groups of step 3

2011/05/04 by Kang-Hai Tan, Xiaoping Yang, Tan, Kanghai +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1105.0844

openalex publication_date 2011/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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