scholarly journals On the Schrödinger map for regular helical polygons in the hyperbolic space

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 84-109
Author(s):  
Sandeep Kumar
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Three Dimensional ◽  
Smooth Solutions ◽  
Straight Line ◽  
Dimensional Minkowski Space ◽  
Polygonal Curve ◽  
Schrödinger Map ◽  
Theoretical Results ◽  
Nonzero Torsion

Abstract The main purpose of this article is to understand the evolution of X t = X s ∧− X ss , with X(s, 0) a regular polygonal curve with a nonzero torsion in the three-dimensional Minkowski space. Unlike in the case of the Euclidean space, a nonzero torsion now implies two different helical curves. This generalizes recent works by the author with de la Hoz and Vega on helical polygons in the Euclidean space as well as planar polygons in the Minkowski space. Numerical experiments in this article show that the trajectory of the point X(0, t) exhibits new variants of Riemann’s non-differentiable function whose structure depends on the initial torsion in the problem. As a result, we observe that the smooth solutions (helices, straight line) in the Minkowski space show the same instability as displayed by their Euclidean counterparts and curves with zero-torsion. These numerical observations are in agreement with some recent theoretical results obtained by Banica and Vega.

scholarly journals $d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$

2021 ◽  
Vol 52 (1) ◽  
pp. 37-67
Author(s):  
Yuichiro Sato
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Three Dimensional ◽  
Representation Formula ◽  
Degenerate Metric ◽  
Dimensional Minkowski Space ◽  
One To One ◽  
Zero Mean Curvature

In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $d$-minimal surfaces in $\mathbb{R}^{0,2,1}$ and spacelike flat zero mean curvature (ZMC) surfaces in four-dimensional Minkowski space $\mathbb{R}^{4}_{1}$ are in one-to-one correspondence.

scholarly journals The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 4
Author(s):  
Erhan Güler
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Algebraic Surfaces ◽  
Cartesian Coordinates ◽  
Maximal Surfaces ◽  
Dimensional Minkowski Space ◽  
The Family

We consider the Enneper family of real maximal surfaces via Weierstrass data (1,ζm) for ζ∈C, m∈Z≥1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E2,1. Moreover, we propose that the family has degree (2m+1)2 (resp., class 2m(2m+1)) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry

2009 ◽  
Vol 50 (5) ◽  
pp. 053507 ◽  
Author(s):  
Joshua T. Horwood ◽  
Raymond G. McLenaghan ◽  
Roman G. Smirnov
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Cartan Geometry ◽  
Dimensional Minkowski Space

Constructions of spacelike Bézier Surfaces in the Three-dimensional Minkowski space

2009 ◽  
Author(s):  
Georgi H. Georgiev ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

Accretive growth kinematics in Minkowski 3-space

2017 ◽  
Vol 14 (05) ◽  
pp. 1750069
Author(s):  
Gül Tuğ ◽  
Zehra Özdemi̇r ◽  
Selçuk Han Aydin ◽  
Fai̇k Nejat Ekmekci̇
Keyword(s):  
Minkowski Space ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

In this study, a model of accretive growth for arbitrary surfaces in three-dimensional Minkowski space is formulated by evolving a curve. An analytical approach to surfaces is also given in terms of a few parameters which are effective in the accretive growth of surfaces. The proposed method is visualized on some test surfaces and displayed in terms of figures.

scholarly journals 3d conformal fields with manifest sl(2, ℂ)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dmitry Ponomarev
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Helicity Formalism ◽  
Natural Connection ◽  
Conformal Fields ◽  
Dimensional Minkowski Space ◽  
Poincaré Algebra ◽  
Massless Fields ◽  
Weight Modules

Abstract In the present paper we construct all short representation of so(3, 2) with the sl(2, ℂ) symmetry made manifest due to the use of sl(2, ℂ) spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS4 suggested earlier. We then study unitarity of the resulting representations, identify them as the lowest-weight modules and as conformal fields in the three-dimensional Minkowski space. Finally, we compare these results with the existing literature and discuss the properties of these representations under contraction of so(3, 2) to the Poincare algebra.

Sign in / Sign up

Export Citation Format

Share Document