Results 201 to 210 of about 71,381 (220)

ABNORMAL SUBANALYTIC DISTRIBUTIONS IN SUB-RIEMANNIAN GEOMETRY

Ludovic Rifford, Adam Parusiński, André Belotto da Silva   +2 more
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The tangent space in sub-riemannian geometry

Journal of Mathematical Sciences, 1994
Let \(M\) be a sub-Riemannian manifold. Suppose that the Hörmander condition holds. Then to each point \(p\in M\) we can associate its degree of nonholonomy \(r(p)\) which counts how many bracket iterations of horizontal vector fields near \(p\) are needed to span the tangent space \(T_pM\).
A. Bellaïche
semanticscholar   +3 more sources

Introduction to geodesics in sub-Riemannian geometry

, 2016
Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds.
A. Agrachev, D. Barilari, U. Boscain
semanticscholar   +4 more sources

Sub-Riemannian Geometry and Optimal Transport

, 2014
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the ...
L. Rifford
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The Sub-Riemannian Geometry of Screw Motions with Constant Pitch

Journal of Geometric Analysis, 2023
We consider a family of Riemannian manifolds M such that for each unit speed geodesic γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Eduardo Hulett, R. P. Moas, M. Salvai
semanticscholar   +1 more source

Sub-Riemannian Geometry

2009
Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context.
Ovidiu Calin, Der-Chen Chang
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Characterizations of hamiltonian geodesics in sub-riemannian geometry

Journal of Dynamical and Control Systems, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alcheikh, M., Orro, P., Pelletier, F.
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Sub-Riemannian geometry and nonholonomic mechanics

AIP Conference Proceedings, 2011
The purpose of the present paper is to study the geometry of a sub‐Riemannian manifold and to apply the results to the nonholonomic mechanical systems. First, we construct a linear connection on the horizontal distribution and obtain some Bianchi identities for it.
Aurel Bejancu, Viorel Barbu, Ovidiu Ca^rjǎ   +2 more
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Curvature in sub-Riemannian geometry

Journal of Mathematical Physics, 2012
We study curvature problems on a nearly Riemannian manifold, which is a sub-Riemannian manifold (M, HM, g, VM) whose adapted tensor field given by (2.2) vanishes identically. First, we prove the existence and uniqueness of what we call horizontal Riemannian connection, which is a torsion-free and metric linear connection ∇ on the horizontal ...
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Foucault pendulum and sub-Riemannian geometry

Journal of Mathematical Physics, 2010
The well known Foucault nonsymmetrical pendulum is studied as a problem of sub-Riemannian geometry on nilpotent Lie groups. It is shown that in a rotating frame a sub-Riemannian structure can be naturally introduced. For small oscillations, three dimensional horizontal trajectories are computed and displayed in detail.
Anzaldo-Meneses, A., Monroy-Pérez, F.
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