2024-03-062024-03-062024-01-26Muñoz González, Alejandra. Classificação de superfícies de translação, homotéticas e separáveis com curvaturas constantes no espaço euclidiano. 2024. 83 f. Dissertação (Mestrado em Matemática) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.http://repositorio.bc.ufg.br/tede/handle/tede/13298In this work, we study some classes of surfaces with constant Gaussian (K) or mean curvature (H) in Euclidean space R3. In the first part, we investigate surfaces obtained as the sum of two curves or as graphs of the product of two functions. We consider the problem of finding all surfaces of these types with constant Gaussian curvature (CGC).We extend the results to non-degenerate surfaces in Lorentz-Minkowski space. In the second part, we consider surfaces with constant Gaussian curvature given by an implicit equation of the form f (x) + g(y) + h(z) = 0, where f , g, and h are real functions of one variable. If K = 0, we show that the surface is a surface of revolution, a cylindrical surface, or a conical surface, obtaining explicit parametrizations of these surfaces. If K ̸= 0, the surface is a surface of revolution. KeywordsAttribution-NonCommercial-NoDerivatives 4.0 InternationalSuperfícies de translaçãoSuperfícies homotéticasSuperfícies separáveisSuperfícies homotéticas mínimasCurvatura Gaussiana constanteCurvatura média constanteTranslation surfacesHomothetic surfacesSeparable surfacesMinimal homothetic surfacesConstant Gaussian curvatureConstant mean curvatureCIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIALDissertação