Results 1 to 10 of about 873 (174)

A Formula for Popp’s Volume in Sub-Riemannian Geometry [PDF]

open access: greenAnalysis 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   +7 more sources

A connection theoretic approach to sub-Riemannian geometry [PDF]

open access: greenJournal of Geometry and Physics, 2003
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. In particular, some necessary and sufficient conditions for the existence of abnormal extremals will be derived.
Bavo Langerock
openalex   +5 more sources

On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection

open access: diamondДифференциальная геометрия многообразий фигур, 2023
In this article, a sub-Riemannian manifold of contact type is under­stood as a Riemannian manifold equipped with a regular distribution of codimension-one and by a unit structure vector field orthogonal to this distribution. This vector field is called a
S. V. Galaev
doaj   +2 more sources

Sub-Riemannian geometry on infinite-dimensional manifolds [PDF]

open access: greenThe Journal of Geometric Analysis, 2012
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.
Erlend Grong   +2 more
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On the role of abnormal minimizers in sub-riemannian geometry [PDF]

open access: bronzeAnnales 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.
Bernard Bonnard, Emmanuel Trélat
openalex   +7 more sources

Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase [PDF]

open access: yesJournal 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

Sub-Riemannian geometry of the coefficients of univalent functions [PDF]

open access: greenJournal of Functional Analysis, 2006
19 ...
Irina Markina   +2 more
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An Inverse Problem from sub-Riemannian geometry [PDF]

open access: bronzePacific Journal of Mathematics, 2003
The geodesics for a sub-Riemannian metric on a three-dimensional contact manifold $M$ form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on $M$, locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish.
Thomas Ivey
openalex   +4 more sources

Connections and Curvature in sub-Riemannian geometry

open access: green, 2009
For a subRiemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection on strictly pseudoconvex CR manifolds.
Robert K. Hladky
openalex   +4 more sources

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