On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1
نویسندگان
چکیده
منابع مشابه
On 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 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 THE LIFTS OF SEMI-RIEMANNIAN METRICS
In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...
متن کاملOn 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 کاملShortest Paths for Sub-riemannian Metrics on Rank-two Distributions
We study length-minimizing arcs in sub-Riemannian manifolds (M;E;G) whose metric G is de ned on a rank-two bracket-generating distribution E. It is well known that all length-minimizing arcs are extremals, and that these extremals are either \normal" or \abnormal." Normal extremals are locally optimal, in the sense that every su ciently short piece of such an extremal is a minimizer. The questi...
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: Journal of Mathematical Sciences
سال: 2006
ISSN: 1072-3374,1573-8795
DOI: 10.1007/s10958-006-0151-5