Results 1 to 10 of about 732 (169)
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 +5 more sources
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 +2 more
doaj +3 more sources
Sub-Riemannian Curvature in Contact Geometry [PDF]
Journal of Geometric Analysis, 2016 31 pages, 2 figures; v2: the Bonnet-Myers theorem 1.7 now holds for any contact structure; v3: final version (with expanded introduction) to appear on Journal of Geometric Analysis; v4: fixed ...
Andrei Agrachev +2 more
exaly +4 more sources
Shortest and straightest geodesics in sub-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2020 There are many equivalent definitions of Riemannian geodesics. They are naturally generalised to sub-Riemannian manifold, but become non-equivalent. We give a review of different definitions of geodesics of a sub-Riemannian manifold and interrelation between them.
Dmitri V Alekseevsky
exaly +4 more sources
Sub-Riemannian Geometry on Infinite-Dimensional Manifolds [PDF]
Journal of Geometric Analysis, 2014 37pp
Erlend Grong +2 more
exaly +4 more sources
Sub-Riemannian Geometry and Geodesics in Banach Manifolds [PDF]
Journal of Geometric Analysis, 2019 In this paper, we define and study sub-Riemannian structures on Banach manifolds. We obtain extensions of the Chow-Rashevski theorem for exact controllability, and give conditions for the existence of a Hamiltonian geodesic flow despite the lack of a Pontryagin Maximum Principle in the infinite dimensional setting.
Sylvain Arguillere
exaly +4 more sources
Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry [PDF]
SIAM Journal on Applied Mathematics, 2018 From the point of view of the theory of the partial differential equations, the paper is concerned with the Helmholtz version of the Grushin equation \[ (\partial^2_x+ x^{2r}\partial^2_y) u+ \rho^2u= 0,\quad r=1,2,\dots, \] which, by separation of variables, reduces to the analysis of eigenfunctions of anisotropic harmonic oscillators.
Allan Greenleaf +2 more
exaly +5 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.
Mietton, T., Rizzi, L.
openaire +4 more sources
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
openaire +2 more sources
Advanced Nonlinear Studies, 2022 In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa +2 more
doaj +1 more source