Doutorado em Matemática (IME)
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Navegando Doutorado em Matemática (IME) por Assunto "Aplicação normal de Gauss prescrita"
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Item Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano(Universidade Federal de Goiás, 2014-09-29) Dias, D. G.; Corro, Armando M.V.; http://lattes.cnpq.br/4498595305431615; Corro, Armando M.V.; Piccione, Paolo; Dorea, Chang C.Y.; Ferreira, W.; Adriano, LeviWe present hypersurfaces with prescribed normal Gauss map. These surfaces are obtained as the envelope of a sphere congruence where the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, the Appell’s surfaces and the Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGW-surfaces applying inversions and dilatations. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSGW-surfaces). As application we classify the EDSGW-surfaces of rotation and present a 4-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes. We generalized the EDSGW-surfaces for the case of hypersurfaces in Rn+1, n ≥ 2. We present a representation for these hypersurfaces in the case where the stereographic projection of the normal Gauss map N is given by the identity application. As an application, we will characterize the rotational examples.Item Classes de hipersuperfícies Weingarten generalizadas tipo Laguerre(Universidade Federal de Goiás, 2017-12-07) Ruys, Wesley da Silva; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Riveros, Carlos Maber Carrion; Adriano, Levi Rosa; Velásquez, Marco Antonio Lázaro; Pina, Romildo da SilvaIn this work we present a classification of the Laguerre minimal surfaces with flat curvature lines. We introduce three classes of hypersurfaces that generalize the Laguerre minimal surfaces with the prescribed Gaussian normal application. The first class is associated to biharmonic applications and is related by a Legendre transformation to hypersurfaces that in the isotropic model has harmonic isotropic mean curvature. As an application, we classify the hypersurfaces of rotation and we present examples of these hypersurfaces parameterized by flat curvature lines. We obtain a characterization of the other two classes of hypersurfaces, we study the rotation ones and we present examples.