Results 1 to 10 of about 261,982 (261)

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
doaj   +9 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   +5 more sources

Sub-Riemannian Geometry of Curves and Surfaces in Roto-Translation Group Associated with Canonical Connection [PDF]

Mathematics
The 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

Control of Nonholonomic Systems and Sub-Riemannian Geometry [PDF]

, 2013
Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon ...
Jean, Frederic
core   +7 more sources

Model spaces in sub-Riemannian geometry [PDF]

Communications in Analysis and Geometry, 2016
We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense that any linear isometry between the horizontal tangent spaces is realized by a global isometry.
Erlend Grong
semanticscholar   +9 more sources

Topics in sub-Riemannian geometry [PDF]

Russian Mathematical Surveys, 2016
This thesis is concerned with three different problems in sub-Riemannian geometry faced during my PhD. The first one is a problem in differential geometry and is about the local conformal classification of a certain class of sub-Riemannian structures. In
Boarotto, Francesco
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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, Sorin Dragomir, Francesco Esposito   +2 more
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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
openalex   +3 more sources

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 geodesic means that it contains a non-trivial abnormal subsegment.
Thomas Mietton, L. Rizzi
semanticscholar   +9 more sources