Results 31 to 40 of about 70,602 (222)
Sub-Riemannian Geometry on Infinite-Dimensional Manifolds [PDF]
The Journal of Geometric Analysis, 2014 We generalize the concept of sub-Riemannian geometry to infinite-dimensional manifolds modeled on convenient vector spaces. On a sub-Riemannian manifold $M$, the metric is defined only on a sub-bundle $\calH$ of the tangent bundle $TM$, called the horizontal distribution.
Irina Markina +2 more
openaire +5 more sources
Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase [PDF]
Journal of Imaging, 2021 We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex.
Emre Baspinar
doaj +2 more sources
On the role of abnormal minimizers in sub-riemannian geometry [PDF]
Annales de la faculté des sciences de Toulouse Mathématiques, 2001 Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^ )$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.
Bonnard, Bernard, Trélat, Emmanuel
openaire +6 more sources
On Jacobi fields and canonical connection in sub-Riemannian geometry [PDF]
, 2015 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 ...
D. Barilari, L. Rizzi
semanticscholar +7 more sources
Constant curvature models in sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2017 The second version reflected comments from the reviewing process. Introduction and parts of exposition are extended, some proofs made more precise.
D. Alekseevsky, A. Medvedev, J. Slovák
semanticscholar +4 more sources
Bakry–Émery curvature and model spaces in sub-Riemannian geometry [PDF]
Mathematische Annalen, 2019 We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a ...
D. Barilari, L. Rizzi
semanticscholar +4 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 +4 more sources
, 2004 This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups.
Buliga, Marius
core +4 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 ...
S. Arguillère
semanticscholar +7 more sources
Sub-Riemannian geometry of the coefficients of univalent functions [PDF]
Journal of Functional Analysis, 2007 19 ...
Dmitri Prokhorov +2 more
openaire +4 more sources