Results 1 to 10 of about 71,381 (220)
Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, copepod nauplii and copepod robot [PDF]
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 +3 more sources
Curvature and the equivalence problem in sub-Riemannian geometry [PDF]
Archivum Mathematicum, 2022 These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry.
Erlend Grong
semanticscholar +6 more sources
Sub-Riemannian Geometry and Geodesics in Banach Manifolds [PDF]
The Journal of Geometric Analysis, 2019 In this paper, we define and study sub-Riemannian structures on Banach manifolds. We obtain extensions of the Chow–Rashevsky Theorem for exact controllability, and give conditions for the existence of a Hamiltonian geodesic flow despite the lack of a ...
Sylvain Arguillère
semanticscholar +8 more sources
Sub-Riemannian Geometry of Curves and Surfaces in Roto-Translation Group Associated with Canonical Connection [PDF]
MathematicsThe aim of this paper is to obtain the sub-Riemannian properties of the roto-translation group RT. At the same time, we compute the sub-Riemannian limits of Gaussian curvature associated with two kinds of canonical connections for a C2-smooth surface in ...
Han Zhang, Haiming Liu
doaj +3 more sources
On Jacobi fields and canonical connection in sub-Riemannian geometry [PDF]
, 2017 In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in ...
Barilari, Davide, Rizzi, Luca
core +7 more sources
C-R Immersions and Sub-Riemannian Geometry
Axioms, 2023 On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form θ, we consider natural ϵ-contractions, i.e., contractions gϵM of the Levi form Gθ, such that the norm of the Reeb vector field T of (M, θ) is ...
Elisabetta Barletta +2 more
doaj +2 more sources
Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry [PDF]
Advanced Nonlinear Studies, 2022 In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa +2 more
doaj +2 more sources
Journal of Differential Geometry, 1986 A sub-Riemannian or singular Riemannian geometry is given by a smoothly varying positive definite quadratic form defined only on a subbundle \(S\) of the tangent bundle \(TM\) of a differentiable manifold, \(S\) being bracket-generating, that is sections of \(S\) together with their Lie brackets generate the \(C^{\infty}(M)\)-module \(V(M)\) of vector ...
Robert S. Strichartz
openalex +3 more sources
Branching Geodesics in Sub-Riemannian Geometry [PDF]
Geometric and Functional Analysis, 2020 In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal ...
Thomas Mietton, L. Rizzi
semanticscholar +6 more sources
A Comprehensive Introduction to Sub-Riemannian Geometry [PDF]
, 2019 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or ...
A. Agrachev, D. Barilari, U. Boscain
semanticscholar +4 more sources