On 2-Step, Corank 2, Nilpotent Sub-Riemannian Metrics
نویسندگان
چکیده
منابع مشابه
On 2-step, corank 2 nilpotent sub-Riemannian metrics
In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics that are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical H...
متن کاملOn the Spherical Hausdorff Measure in Step 2 Corank 2 Sub-Riemannian Geometry
In this paper, we consider generic corank 2 sub-Riemannian structures, and we show that the Spherical Hausdorf measure is always a C-smooth volume, which is in fact generically Csmooth out of a stratified subset of codimension 7. In particular, for rank 4, it is generically C 2 . This is the continuation of a previous work by the auhors. subjclass: 53C17, 49J15, 58C35
متن کاملun 2 00 4 On geodesic equivalence of Riemannian metrics and sub - Riemannian metrics on distributions of corank 1 Igor
The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...
متن کاملOn geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1
The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...
متن کاملRiemannian Submersions and Lattices in 2-step Nilpotent Lie Groups
We consider simply connected, 2-step nilpotent Lie groups N, all of which are diffeomorphic to Euclidean spaces via the Lie group exponential map exp : ˆ → N. We show that every such N with a suitable left invariant metric is the base space of a Riemannian submersion ρ : N* → N, where the fibers of ρ are flat, totally geodesic Euclidean spaces. The left invariant metric and Lie algebra of N* ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2012
ISSN: 0363-0129,1095-7138
DOI: 10.1137/110835700