Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Por Orientador "Adriano, Levi Rosa"
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Item Superfícies isocurvadas no semiespaço Euclidiano tridimensional(Universidade Federal de Goiás, 2017-03-31) García, Hector Andrés Rosero; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Roitman, Pedro; Pina, Romildo da SilvaIn this work we develop the basics of the concept of Isocurved Surface, introduced in [2] by Barroso and Roitman, that is, a surface immersed in a 3-dimensional manifold M and which have the same Gaussian curvature induced by two different metrics. Later on, we show a geometric method to generate non-trivial examples of elliptic and hyperbolic isocurved surfaces for the particular case of M = R3+ and the Euclidean and hyperbolic metrics induced on it. We also exhibit some examples coming from the geometric method above.Item Classificação de superfícies de translação, homotéticas e separáveis com curvaturas constantes no espaço euclidiano(Universidade Federal de Goiás, 2024-01-26) Muñoz González, Alejandra; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Ribeiro Júnior, Ernani de Sousa; Leandro Neto, BeneditoIn 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. KeywordsItem Os espaços conformemente flat E3 e F3(Universidade Federal de Goiás, 2019-03-07) Santos, Róbson Lousa dos; Pereira, Rosane Gomes; http://lattes.cnpq.br/4892810550527855; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Pereira, Rosane Gomes; Pina, Romildo da Silva; Silva, Tarcísio CastroThis work is a bibliographical research based on papers by Armando V. Corro, Romildo da Silva Pina and Marcelo Souza (2011) [7] and Kellcio Oliveira Araujo, Ningwei Cui and Romildo da Silva Pina (2015) [3]. In these papers the surfaces of rotation in the conformal flat space E3 and the helicoidal surfaces in the conformally flat space F3, respectively, are studied. We have shown that the theorems of Efimov and Shlenker, which generalizes the famous Hilbert Theorem, are not vowed in space E3. Furthermore, we characterize most common helicoidal surfaces in F3.Item Classificação e construção de superfícies mínimas de translação em formas espaciais(Universidade Federal de Goiás, 2022-10-27) Silva, Marcos Gomes da; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Tokura, Willian Isao; Corro, Armando Mauro Vasquez; Lima, Ronaldo Freire deA translation surface of Euclidean space is the sum of two regular curves and , called the generating curves. In this paper we classify the minimal translation surfaces of and we give a method of construction of explicit examples. Besides the plane and the minimal surfaces of Scherk type, it is proved that up to reparameterizations of the generating curves, any minimal translation surface is described as , where is a curve parameterized by arc length s, its curvature is a positive solution of the autonomous ODE and its torsion is Here and are constants such that the cubic equation has three real roots , and . Furthermore in the half-space model of hyperbolic space, that is, with the hyperbolic metric, a translation surface that writes as or , where f and g are smooth functions, we prove that the only minimal translation surfaces are totally geodesic planes.Item Rigidez métrica e topológica de hipersuperfícies imersas em formas espaciais(Universidade Federal de Goiás, 2016-03-08) Tokura, Willian Isáo; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Pieterzack, Mauricio Donizetti; Changyu, XiaIn thiswork,wepresentresultsaboutmetricrigiditytheoremsandtopologicalrigidity theorems forclosedhypersurfacesimmersedin Hn+1, Rn+1 and Sn+1. Theseresultswere obtained byQiaolingWangandChangyuXiaandpublishedinTheQuarterlyJournal of Mathematics(2005),ProceedingsoftheEdinburghMathematicalSociety(2006)and CzechoslovakMathematicalJournal(2007).