Results 11 to 20 of about 70,602 (222)
A connection theoretic approach to sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2002 We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism.
Langerock, B.
core +6 more sources
A Formula for Popp’s Volume in Sub-Riemannian Geometry [PDF]
Analysis and Geometry in Metric Spaces, 2013 Abstract For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian ...
Barilari Davide, Rizzi Luca
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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.
E. Grong
semanticscholar +5 more sources
Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]
Calc Var Partial Differ Equ, 2023 We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and ...
Don S, Magnani V.
europepmc +5 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
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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Homogeneous geodesics in sub-Riemannian geometry [PDF]
ESAIM: 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.
Alexey Podobryaev
semanticscholar +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 +7 more sources
The Relative Heat Content for Submanifolds in Sub-Riemannian Geometry [PDF]
Séminaire de théorie spectrale et géométrie, 2022 We study the small-time asymptotics of the relative heat content for submanifolds in sub-Riemannian geometry. First, we prove the existence of a smooth tubular neighborhood for submanifolds of any codimension, assuming they do not have characteristic ...
Tommaso Rossi
semanticscholar +3 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