Results 21 to 30 of about 892 (193)

Integral Formulas for Almost Product Manifolds and Foliations

Mathematics, 2022
Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral formulas for almost multi-product manifolds, foliations and multiply twisted products of Riemannian, metric-affine and sub-Riemannian manifolds, to ...
Vladimir Rovenski
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Bicycle paths, elasticae and sub-Riemannian geometry [PDF]

Nonlinearity, 2021
Abstract We relate the sub-Riemannian geometry on the group of rigid motions of the plane to ‘bicycling mathematics’. We show that this geometry’s geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or straight lines, and that its infinite minimizing geodesics (or ‘metric lines’) correspond ...
Richard Montgomery, Yuri L. Sachkov, Gil Bor, A. A. Ardentov, Enrico Le Donne, Enrico Le Donne   +5 more
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Intrinsic fractional Taylor formula

Bruno Pini Mathematical Analysis Seminar, 2022
We consider a class of non-local ultraparabolic Kolmogorov operators and a suitable fractional Holder spaces that take into account the intrinsic sub-riemannian geometry induced by the operators.
Maria Manfredini
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On the Hausdorff volume in sub-Riemannian geometry [PDF]

Calculus of Variations and Partial Differential Equations, 2011
For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function.
Agrachev, Andrey, BARILARI D, BOSCAIN U.
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Sub-Riemannian geometry of parallelizable spheres [PDF]

Revista Matemática Iberoamericana, 2011
The first aim of the present paper is to compare various sub-Riemannian structures over the three dimensional sphere S^3 originating from different constructions. Namely, we describe the sub-Riemannian geometry of S^3 arising through
Godoy Molina , Mauricio, Markina , Irina
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Sub-Riemannian Geometry of Stiefel Manifolds [PDF]

SIAM Journal on Control and Optimization, 2014
In the paper we consider the Stiefel manifold $V_{n;k}$ as a principal $U(k)$- bundle over the Grassmann manifold and study the cut locus from the unit element. We gave the complete description of this cut locus on $V_{n;1}$ and presented the sufficient condition on the general case. At the end, we study the complement to the cut locus of $V_{2k;k}$.
Christian Autenried, Irina Markina
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A Comprehensive Introduction to Sub-Riemannian Geometry [PDF]

, 2019
Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several ...
Agrachev, Andrei, Barilari, Davide, Boscain, Ugo   +2 more
openaire   +3 more sources

Characteristic Laplacian in Sub-Riemannian Geometry [PDF]

International Mathematics Research Notices, 2015
We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms in a complex setting.
Jeremy Daniel, Xiaonan Ma
openaire   +3 more sources

The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss-Bonnet Theorem in the Group of Rigid Motions of Minkowski Plane with General Left-Invariant Metric

Journal of Function Spaces, 2021
The group of rigid motions of the Minkowski plane with a general left-invariant metric is denoted by E1,1,gλ1,λ2, where λ1≥λ2>0. It provides a natural 2-parametric deformation family of the Riemannian homogeneous manifold Sol3=E1,1,g1,1 which is the ...
Jianyun Guan, Haiming Liu
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Integral Formulas for a Foliation with a Unit Normal Vector Field

Mathematics, 2021
In this article, we prove integral formulas for a Riemannian manifold equipped with a foliation F and a unit vector field N orthogonal to F, and generalize known integral formulas (due to Brito-Langevin-Rosenberg and Andrzejewski-Walczak) for foliations ...
Vladimir Rovenski
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