Translation and homothetical surfaces in Euclidean space with constant curvature

TL;DR

This paper classifies surfaces in Euclidean and Lorentz-Minkowski spaces formed by specific functions or sums of curves that have constant Gauss curvature, expanding understanding of their geometric properties.

Contribution

It provides a complete classification of such surfaces with constant curvature, including extensions to Lorentz-Minkowski space.

Findings

Classification of Euclidean surfaces with constant Gauss curvature

Extension of results to Lorentz-Minkowski space

Identification of specific forms of surfaces with constant curvature

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.