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math.DG2015★ 1 cited
Extremals in the Engel group with a sub-Lorentzian metric
Andrey Ardentov, Tiren Huang, Yuri L. Sachkov +1
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we fi…
math.DG2012
On Regularity of Abnormal Subriemannian Geodesics
Kanghai Tan, Xiaoping Yang
We prove the smoothness of abnormal minimizers of subriemannian manifolds of step 3 with a nilpotent basis. We prove that rank 2 Carnot groups of step 4 admit no strictly abnormal…
math.DG2011★ 1 cited
SubRiemannian geodesics for Carnot groups of step 3
Kanghai Tan, Xiaoping Yang
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.…