scholarly journals Classifications of translation surfaces in isotropic geometry with constant curvature

2020 ◽  
Vol 72 (3) ◽  
pp. 291-306
Author(s):  
M. E. Aydin
Keyword(s):  
Constant Curvature ◽  
Arbitrary Constant ◽  
Translation Surfaces

UDC 515.12 We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvatures underthe condition that at least one of translating curves lies in a plane.

scholarly journals Polynomial affine translation surfaces in Euclidean 3-space

2017 ◽  
Vol 37 (3) ◽  
pp. 195
Author(s):  
Hülya Gün Bozok ◽  
Mahmut Ergüt
Keyword(s):  
Constant Curvature ◽  
Existence Results ◽  
Translation Surfaces ◽  
Affine Translation

In this paper we study the polynomial affine translation surfaces in E3with constant curvature. We derive some non-existence results for suchsurfaces. Several examples are also given by figures.

scholarly journals Constant Curvature Translation Surfaces in Galilean 3-Space

2019 ◽  
Vol 12 (1) ◽  
pp. 9-19
Author(s):  
Muhittin Evren AYDIN ◽  
Mihriban Alyamaç KÜLAHÇI ◽  
Alper Osman ÖĞRENMİŞ
Keyword(s):  
Constant Curvature ◽  
Translation Surfaces

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

scholarly journals Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
James Kohout ◽  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Constant Curvature ◽  
Harmonic Map ◽  
Gradient Flow ◽  
Minimal Immersion ◽  
Curvature Surface ◽  
Previous Theory ◽  
Target Manifold ◽  
Harmonic Map Flow

AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.

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