Related papers: A Three-Dimensional Laguerre Geometry and Its Visu…
Variationality of the equation of conformal geodesics is an important problem in geometry with applications to general relativity. Recently it was proven that, in three dimensions, this system of equations for un-parametrized curves is the…
The 3-dimensional coherence matrix is interpreted by emphasising its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the…
Starting with the classical circle geometry of Sophus Lie, we give a survey about some of the developments in the area of chain geometries during the last three decades.
The triangulations of a regular convex polygon are enumerated according to the number of diagonals parallel to a fixed edge. The enumeration uses the Shapiro convolution identity, as well as an interpretation of this identity in terms of…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
When a linear chain of plasmonic nano-particles is exposed to a transverse DC magnetic field, the chain modes are elliptically polarized, in a single plane parallel to the chain axis; hence, a novel longitudinal plasmon-rotation is created.…
We consider a Weyl-Lorentz-$U(1)$-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the so-called symmetric teleparallel geometry, in three dimensions. Firstly,…
The article presents a general concept of the organization of pseudo three dimension visualization of graphics and video content for three dimension visualization systems. The steps of algorithms for solving the problem of synthesis of…
We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable…
In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree $n$ over a finite chain ring $ R.$ We extend the concepts of $ n $-isometry and $ n $-equivalence known for constacyclic codes to this class of…
We calculate the intersection ring of three-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold's underlying graph is a tree. We are able to use this…
We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian…
In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner…
This article gives a description of the diagonal $GL_3$-orbits on the quadruple projective variety $(\mathbb P^2)^4$. We give explicit representatives of orbits, and describe the closure relations of orbits. A distinguished feature of our…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization…
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…
We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are…
We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ $U(1)$ gauge theories coupled with a single chiral multiplet. One example is the case where $U(1)$ gauge group has the…