Superfícies de Weingarten regradas em geometrias de Thurston - Viveiros, Anderson Felipe (Universidade Federal de São Carlos, 2025)
In this work, we classify all the ruled Weingarten surfaces of class C³ immersed in the Heisenberg group Nil_3, obtaining explicit parametrizations for each case. We also classify translation surfaces of the graph type in Nil_3 which are linear-Weingarten or whose norm of the second fundamental form is constant. We also classify ruled Weingarten surfaces in the product spaces, S²×R and H²×R. In the space SL_2(R)~, we did an initial study in which we classified vertical and horizontal ruled surfaces whose one of the curvatures, either mean or gaussian, is constant. We included yet a chapter considering Bishop surfaces (or Monge surfaces) in R³, in which we classified all such surfaces of class C² satisfying some polynomial Weingarten relation.
Ruled Weingarten surfaces in Thurston geometries
Keywords: Superfícies de Weingarten; Superfícies regradas; Grupo de Heisenberg; Espaços produto; Grupo linear especial; Weingarten surfaces; Ruled surfaces; Heisenberg group; Product spaces; Special linear group; CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL