Results 1 to 10 of about 892 (193)
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 +7 more sources
A connection theoretic approach to sub-Riemannian geometry [PDF]
Journal 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
Дифференциальная 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]
The 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
openalex +5 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.
Bernard Bonnard, Emmanuel Trélat
openalex +7 more sources
Model spaces in sub-Riemannian geometry [PDF]
Communications in Analysis and Geometry, 2016 25 pages.
Erlend Grong
openalex +6 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
Sub-Riemannian geometry of the coefficients of univalent functions [PDF]
Journal of Functional Analysis, 2006 19 ...
Irina Markina +2 more
openalex +4 more sources
An Inverse Problem from sub-Riemannian geometry [PDF]
Pacific 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
, 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