Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Por Orientador "Corro, Armando Mauro Vasquez"
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Item Superfícies translacionais no espaço isotrópico(Universidade Federal de Goiás, 2019-03-01) Andrade, Thamara Policarpo Mendes de; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Pereira, Rosane Gomes; Carretero, José Luis TeruelTranslation Surfaces are obtained by translating curves contained in non-parallel planes. In this paper, the results of the Aydin, M. E; Ergut, M. Affine Translation Surfaces in the Isotropic Space [3]. Are considered the Affine Translation Surfaces type 1 in the Isotropic 3- Space I3, obtained for translating of two curves in the planes not necessarily orthogonal. The objective was to characterize the Weingarten Affine Translation Surfaces, which satisfy certain conditions with respect to Gaussian and mean curvatures. In addition, results were obtained for Translation Surfaces satisfying \Delta _{I,II }ri = \lambda_{i}ri, finding explicit solutions for the parameterization of such surfaces. Some examples are presented, as well as their respective graphs that were plotted using the Mathematical software.Item A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3(Universidade Federal de Goiás, 2015-02-27) Argote, Fernando Arnulfo Zuñiga; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Santos, João Paulo dos; Pieterzack, Maurício DonizettiIn this work we refer to the study of a geometric invariant surfaces immersed in Euclidean 3-dimensional sphere S3. Such invariant, known as angle contact, is the complementary angle between the distribution of contact d and the tangent space of the surface. Montes and Verderesi [22] characterized the minimal surfaces in S3 with constant contact angle and Almeida, Brazil and Montes [4] studied some properties of immersed constant mean curvature into a round sphere S3 with constant contact angle. The our aim of this work is to deduce a general formula involving the Gaussian curvature, the mean curvature and the contact angle of surfaces immersed in Euclidean sphere 3-dimensional, which shows that the surface is flat if the contact angle is constant. Moreover, we deduce that the Clifford tori are the unique compact surfaces with constant mean curvature having such propriety. KeywordsItem Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico(Universidade Federal de Goiás, 2013-09-20) Fernandes, Karoline Victor; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615In this work we study surfaces M in hyperbolic space whose mean curvature H and Gaussian curvature KI satisfy the relation 2(H 1)e2μ +KI(1e2μ) = 0; where μ is a harmonic function with respect to the quadratic form s = KII + 2(H 1)II; and I, II denote, respectively, the first and second quadratic form of M. These surfaces are called Generalized Weingarten surfaces of harmonic type (HGW-surfaces). We obtain a representation type Weierstrass for these surfaces that depend on three holomorphic functions. As an application we obtain a representation type Weierstrass for Bryant surfaces and classify all HGW-surfaces of rotation.Item Hipersuperfícies no espaço hiperbólico associadas à equação da curvatura escalar constante(Universidade Federal de Goiás, 2014-03-07) Machado, Cid Dias Ferraz; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Montes, Rodrigo Ristow; Souza, Marcelo Almeida deIn this work we present a study of a class of oriented hypersurfaces in hyperbolic space satisfying a special linear relation between the rth mean curvatures which is based on a Walterson Ferreira and Pedro Roitman’s article, where this class is characterized by a harmonic map derived from the two hyperbolic Gauss maps.We also show the relation of such hypersufaces with solutions of the equation Du+kun+2 n2 = 0, where k 2 f1;0;1g.Item Parametrização de uma hipersuperfície via função suporte no espaço hiperbólico(Universidade Federal de Goiás, 2018-02-26) Mendez, Milton Javier Cárdenas; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Riveros, Carlos Maber Carrión; Pereira, Rosane GomesFirst objective will revise the hyperbolic Gauss map for hypersurfaces Mn C Hn+1 and its relation with tangent horospheres. We will introduce horospherical ovaloids as compact hypersurfaces with regular hyperbolic Gauss map and analyze their properties, analyzes the possible formulations of the Christoffel problem in Hn+1 and that this leads to the notion of hyperbolic curvature radii. Second objective we will prove that the Nirenberg problem on Sn is equivalent to the Christoffel problem in Hn+1. This equivalence is made explicit by means of a representation formula for hypersurfaces in terms of the hyperbolic Gauss map and the horospherical support function.Item Superfícies mínimas de Laguerre e geometria isotrópica(Universidade Federal de Goiás, 2016-02-29) Reyes, Edwin Oswaldo Salinas; Corro, Armando Mauro Vasquez; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4763521P6; Corro, Armando Mauro Vasquez; Adriano, Levi Rosa; Riveros, Carlos Maber CarrionIn this work we refer to the study of a new method and simple approach to minimal surface Laguerre in isotropic model of Laguerre geometry as the bi-harmonic function graph. We developed the isotropic geometry which studies the geometric properties invariant under certain affine transformations in Euclidean space, and the fundamental elements of Laguerre geometry which are spheres orienteds and plans orienteds, and properties which are invariant on the transformation of Laguerre. In addition, we will show a close relationship between minimal surfaces Laguerre spherical type and isotropic minimal surfaces which are given by the graph of harmonic functions and minimal Euclidean surfaces. Finally, the duality metric in the isotropic space is used to develop an isotropic exchange for minimal surfaces Laguerre in certain Lie transformation of Laguerre minimal surfaces in Euclidean space.