Results 41 to 50 of about 1,124 (81)

Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations [PDF]

arXiv, 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. Part I", math.MG/0210189, available at http://arxiv.org/abs/math.MG/0210189, and "Tangent bundles to sub-Riemannian groups", math.MG/0307342, available at http://arxiv.org/abs ...
arxiv  

Curvature exponent and geodesic dimension on Sard-regular Carnot groups

Analysis and Geometry in Metric Spaces
In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
doaj   +1 more source

On the Gromov non-embedding theorem [PDF]

arXiv, 2023
We develop a new method leading to an elementary proof of a generalization of Gromov's theorem about non existence of H\"older embeddings into the Heisenberg group.
arxiv  

Introduction to metric spaces with dilations [PDF]

arXiv, 2010
This paper gives a short introduction into the metric theory of spaces with dilations.
arxiv  

A characterization of homogeneous three-dimensional CR manifolds [PDF]

arXiv, 2023
We characterize homogeneous three-dimensional CR manifolds, in particular Rossi spheres, as critical points of a certain energy functional that depends on the Webster curvature and torsion of the pseudohermitian structure.
arxiv  

The Ptolemaean Inequality in H--type groups [PDF]

arXiv, 2013
We prove the Ptolemaean Inequality and the Theorem of Ptolemaeus in the setting of $H$--type groups of Iwasawa--type.
arxiv  

Invertible Carnot Groups [PDF]

, 2016
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman, David M.
core  

On the role of embeddability in conformal pseudo-hermitian geometry

Analysis and Geometry in Metric Spaces
In this article, we review some recent results about the role of embeddability in conformal CR (Cauchy-Riemann) geometry. We will show how this condition enters in the second variation of the pseudo-hermitian counterpart of the Einstein-Hilbert action ...
Malchiodi Andrea
doaj   +1 more source

Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds [PDF]

, 2015
In this paper we consider surfaces of class $C^1$ with continuous prescribed mean curvature in a three-dimensional contact sub-Riemannian manifold and prove that their characteristic curves are of class $C^2$.
Galli, Matteo, Ritoré, Manuel
core  

Mok-Siu-Yeung type formulas on contact locally sub-symmetric spaces [PDF]

arXiv, 2007
We derive Mok-Siu-Yeung type formulas for horizontal maps from compact contact locally sub-symmetric spaces into strictly pseudoconvex CR manifolds and we obtain some rigidity theorems for the horizontal pseudoharmonic maps.
arxiv