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Navegando Região Metropolitana de Goiânia (RMG) por Por Orientador "Adriano, Levi Rosa"
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Item Sobre estruturas gradiente Einstein-type produto torcido(Universidade Federal de Goiás, 2022-04-13) Batista, Elismar Dias; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Corro, Armando Mauro Vasquez; Santos, João Paulo dos; Gomes, José Nazareno Vieira; Ribeiro Júnior, Ernani de SousaIn this work, we study gradient Einstein-type structures immersed in a warped product space of an interval I and a Riemannian manifold M, with a potential function h given by the height function. First, we obtained the necessary conditions for an Einstein-type gradient structure immersed in a warped product to be minimal, totally umbilic or totally geodesic. In addition, we provide triviality results for the potential function h. Next, we characterize the rotational hypersurfaces having a gradient Einstein-type structure in warped product, where the fiber is a space form. We also study particular cases of gradient Einstein-type structures in warped product spaces, namely, gradient Ricci-harmonic solitons (GRHS). In this case, we prove triviality results for the potential and warped functions when they reach a maximum or minimum. Finally, we provide a family non-enumerable of non-trivial geodesically complete examples of GRHS considering the base and fiber of a warped product conformal to a semi-Euclidean space invariant under the action of a translation group of codimension one.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 Desigualdades universais para autovalores do polidrifting laplaciano em dominios compactos do R^n e S^n(Universidade Federal de Goiás, 2016-03-08) Pereira, Rosane Gomes; Adriano, Levi Rosa; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4768692Y1; Adriano, Levi Rosa; Pina, Romildo da Silva; Changyu, Xia; Gonçalves, José Vlado Abreu; Barbosa, Ezequiel RodriguesIn this work, we study eigenvalues of poly-drifting laplacian on compact Riemannian manifolds with boundary (possibly empty). Here, we bring a universal inequality for the eigenvalues of the poly-drifting operator on compact domains in an Euclidean spaceRn. Besides,weintroduce universal inequalities for eigenvalues of poly-drifting operator on compact domains in a unit n-sphere Sn. We give an universal inequality for lower order eigenvalues of the poly-drifting operator inRn and Sn. Moreover, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space. Let be a bounded domain in a n-dimensional Euclidean space Rn. We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting laplacian 8>><>>: L u+ (r(divu)r divu) = ¯ u; in ; uj@ = 0 Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived.Item 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 Desigualdade de Caffarelli-Kohn-Nirenberg e solitons de Yamabe gradiente(Universidade Federal de Goiás, 2019-05-31) Tokura, Willian Isao; Adriano, Levi Rosa; http://lattes.cnpq.br/3206466156270217; Adriano, Levi Rosa; Silva, Edcarlos Domingos da; Pina, Romildo da Silva; Sousa, Paulo Alexandre Araújo; Ribeiro Junior, Ernani de SousaThis thesis deals with two distinct problems. Namely, we study [(P1)] Rigidity of metric spaces that support CKN inequality; [(P2)] Gradient Yamabe solitons on top of warped product manifolds B x f F. For the first problem, we prove that the metric measure spaces that support the CKN inequality have n-dimensional volume growth, that is, there exists a universal constant C 0gt; 0 such that, m(B x (ρ)) ≥ C 0 ρ n , ∀x ∈ M, ρ gt; 0. As application, some rigidity theorems are obtained in the following spaces: Riemannian manifolds, Finsler manifolds and Alexandrov spaces. For the second problem, taking a gradient Yamabe soliton (B x f F, g, h, ρ), we obtain triviality results for h and f by means of some hypotheses on the base B. Furthermore, under a hypothesis involving the Ricci curvature of the base Ric gB , we prove estimates for h, f and for scalar curvature scal g , in addition, by means of a warping gradient estimates, we present a beautiful obstruction in the construction of gradient Yamabe solitons on warped product manifolds. Finally, by making use of invariant solution techniques, we classify all steady gradient Yamabe solitons with a conformally flat base that is invariant by the action of a codimension 1 translation group.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).