Related papers: Geometry and dynamics of Engel structures
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
A paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors of lines that would seem to require a discrete space. A class of continuous spaces is presented…
The paper concerns the theory of parabolic equations on a broad class of closed subsets of Euclidean space possessing a kind of tangent structure. A necessary framework for considering evolutionary problems is developed, and fundamental…
We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $\pi/4$.…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that a left Leibniz algebra, all of whose maximal subalgebras are right ideals, is nilpotent. A…
We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…
We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed…
This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and…
This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
The goal of this paper is to study two basic problems of hyperbolic geometry. The first problem is to compare the hyperbolic and Euclidean distances. The second problem is to find hyperbolic counterparts of some basic geometric…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
In [CPPP] it was shown that Engel structures satisfy an existence $h$-principle, and the question of whether a full $h$-principle holds was left open. In this note we address the classification problem, up to Engel deformation, of Cartan…
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
Let M be the interior of a compact 3-manifold with non-empty boundary, and T be an ideal (topological) triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi-angle structures…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.