Translation and homothetical surfaces in Euclidean space with constant curvature

2014/10/09 by López, Rafael, Moruz, Marilena
#53A10 #53C45 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.2512

Abstract

We study surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions. We consider the problem to determine all these surfaces with constant Gauss curvature. We extend the results to non degenerate surfaces in Lorentz-Minkowski space.

Related

• Translation surfaces in Euclidean space with constant Gaussian curvature
• Translation surfaces of linear Weingarten type
• Classification of translation surfaces in ℝ³ with constant sectional curvature
• Classifications of translation surfaces in isotropic geometry with constant curvature
• Constant curvature translation surfaces in Galilean 3-space