1 citations · 2 across the 6 of their papers we have counts for
5 papers · 1 filter
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…
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.…
On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds
Kang-Hai Tan, Xiao-Ping Yang
We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannia…
On sublaplacians of sub-Riemannian manifolds
Kang-Hai Tan
In this note we address a notion of sublaplacians of sub-Riemannian manifolds. In particular for fat sub-Riemannian manifolds we answered the sublaplacian question proposed by R. M…
Convex Functions on Sub-Riemannian Manifolds. I
Kang-Hai Tan
We find a different approach to define convex functions in the sub-Riemannian setting. A function on a sub-Riemannian manifold is nonholonomically geodesic convex if its restrictio…