scholarly journals Wave maps and constant curvature surfaces: singularities and bifurcations

2021 ◽  
pp. 28
Author(s):  
David Brander ◽  
Farid Tari
Keyword(s):  
Constant Curvature ◽  
Wave Maps ◽  
Constant Curvature Surfaces

scholarly journals Constant curvature surfaces in a pseudo-isotropic space

2018 ◽  
Vol 49 (3) ◽  
pp. 221-233 ◽  
Author(s):  
Muhittin Evren Aydin
Keyword(s):  
Constant Curvature ◽  
Local Structure ◽  
Mean Curvature ◽  
Plane Curve ◽  
Surfaces Of Revolution ◽  
Curves And Surfaces ◽  
Isotropic Space ◽  
Constant Curvature Surfaces

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space $\mathbb{I}_{p}^{3}$ that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron for spacelike and timelike curves, respectively. The causal character of all admissible surfaces in $\mathbb{I}_{p}^{3}$ has to be timelike up to its absolute. We introduce the formulas of Gaussian and mean curvature for timelike surfaces in $\mathbb{I}_{p}^{3}$. As applications, we describe the surfaces of revolution which are the orbits of a plane curve under a hyperbolic rotation with constant Gaussian and mean curvature.

Some geometry of constant curvature surfaces

1974 ◽  
Vol 76 (3) ◽  
pp. 601-605 ◽  
Author(s):  
P. G. Lowe ◽  
R. E. Melchers
Keyword(s):  
Reinforced Concrete ◽  
Optimum Design ◽  
Constant Curvature ◽  
Principal Curvature ◽  
Principal Direction ◽  
Concrete Slabs ◽  
Reinforced Concrete Slabs ◽  
Constant Curvature Surfaces

1. Introduction. The optimum design of plane reinforced concrete slabs frequently requires consideration of deflected shapes for the slab such that through every point there is at least one principal curvature (κ1) direction on the deflected surface which is a constant curvature direction. The most interesting cases are those where only one principal direction has this property.

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