Results 21 to 30 of about 70,602 (222)
Bicycle paths, elasticae and sub-Riemannian geometry [PDF]
Nonlinearity, 2020 We relate the sub-Riemannian geometry on the group of rigid motions of the plane to ‘bicycling mathematics’. We show that this geometry’s geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or straight lines,
A. Ardentov +4 more
semanticscholar +6 more sources
On the Hausdorff volume in sub-Riemannian geometry [PDF]
Calculus of Variations and Partial Differential Equations, 2011 For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous
A. Agrachev +30 more
core +7 more sources
Characteristic Laplacian in sub-Riemannian geometry [PDF]
International Mathematics Research Notices, 2013 We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms
Daniel, Jeremy, Ma, Xiaonan
core +3 more sources
Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, copepod nauplii and copepod robot
Pacific Journal of Mathematics for Industry, 2018 The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the
Bernard Bonnard +3 more
doaj +2 more sources
Tangent groupoid and tangent cones in sub-Riemannian geometry [PDF]
Duke mathematical journal, 2022 Let $X_1,\cdots,X_m$ be vector fields satisfying H\"ormander's Lie bracket generating condition on a smooth manifold $M$. We generalise Connes's tangent groupoid, by constructing a completion of the space $M\times M\times \mathbb{R}_+^\times$ using the ...
Omar Mohsen
semanticscholar +3 more sources
On measures in sub-Riemannian geometry [PDF]
Séminaire de théorie spectrale et géométrie, 2017 In \cite{gjha} we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new
R. Ghezzi, F. Jean
semanticscholar +6 more sources
On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection
Дифференциальная геометрия многообразий фигур, 2023 In this article, a sub-Riemannian manifold of contact type is understood as a Riemannian manifold equipped with a regular distribution of codimension-one and by a unit structure vector field orthogonal to this distribution. This vector field is called a
S. V. Galaev
doaj +2 more sources
Shortest and straightest geodesics in sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2020 There are many equivalent definitions of Riemannian geodesics. They are naturally generalised to sub-Riemannian manifold, but become non-equivalent. We give a review of different definitions of geodesics of a sub-Riemannian manifold and interrelation between them.
D. Alekseevsky
semanticscholar +4 more sources
An Inverse Problem from sub-Riemannian geometry [PDF]
Pacific Journal of Mathematics, 2003 The geodesics for a sub-Riemannian metric on a three-dimensional contact manifold $M$ form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on $M$, locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish.
Thomas Ivey
+7 more sources
Model spaces in sub-Riemannian geometry [PDF]
Communications in Analysis and Geometry, 2021 25 pages.
Erlend Grong
openaire +6 more sources