TRANSLATION AND HOMOTHETICAL SURFACES IN EUCLIDEAN SPACE WITH CONSTANT CURVATURE

• DOI: 10.4134/jkms.2015.52.3.523
• Publication Date: 2015-05-21T00:49:25Z
• Authors: Rafael Lopez; Marilena Moruz
• Keywords: Mathematics - Differential Geometry; Differential Geometry (math.DG); Mean curvature; Homothetical surface; FOS: Mathematics; 53A10, 53C45; [MATH] Mathematics [math]; 0101 mathematics; Gauss curvature; 01 natural sciences; Translation surface

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.