Results 1 to 10 of about 71,054 (192)
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
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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
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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
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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
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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
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Curvature and the equivalence problem in sub-Riemannian geometry [PDF]
Archiv der Mathematik, 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
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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
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Steiner and tube formulae in 3D contact sub-Riemannian geometry [PDF]
Communications in Contemporary Mathematics, 2023 We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local nature.
Davide Barilari, Tania Bossio
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Homogeneous geodesics in sub-Riemannian geometry [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2022 We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum.
A. V. Podobryaev
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Sub-Riemannian Geometry and Geodesics in Banach Manifolds [PDF]
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
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