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Sólitons de Ricci Gradiente Steady Localmente Conformemente Flat / On Locally Conformally Flat Gradient Steady Ricci SolitonsReis, Hiuri Fellipe Santos dos 22 March 2013 (has links)
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Previous issue date: 2013-03-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we present a study on locally conformally flat gradient steady Ricci solitons
which is based on a Huai Dong-Cao and Qing Chen’s article, where they was classified
the n-dimensional (n ≥ 3) complete noncompact locally conformally flat gradient steady
Ricci solitons. In particular, we prove that a complete noncompact non-flat locally
conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton. / Neste trabalho apresentamos um estudo dos sólitons de Ricci gradiente steady localmente
conformemente flat, baseado no trabalho de Huai-Dong Cao e Qiang Chen, onde são
classificados os sólitons de Ricci gradiente steady n-dimensionais (n ≥ 3), completos,
não-compactos e localmente conformemente flat. Em particular provamos que um sóliton
de Ricci gradiente steady completo, não-compacto, não-flat e localmente conformemente
flat é, a menos de homotetia, o sóliton de Bryant.
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Sobre rigidez de gradiente quase Ricci Soliton / About rigidity of gradient almost Ricci SolitonGomes, Maria Francisca de Sousa 20 April 2017 (has links)
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Previous issue date: 2017-04-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is based on [1] and aims to show a result of rigidity for gradient almost
Ricci soliton. We will prove that an almost Ricci soliton gradient with nonnegative scalar
curvature, where ∇ f is a non-trivial conformal field, is either a Euclidean space R
n or
the sphere S
n
. Moreover, we have that, in the Spherical case, the potential function is
given by first eigenfunction of the Laplacian. Finally, we will find necessary and sufficient
conditions for that a compact locally conformally flat gradient almost Ricci soliton is
isometric the sphere Sn. / Este trabalho está baseado em [1] e tem por objetivo apresentar um resultado de
rigidez para gradiente quase Ricci soliton. Provaremos que um gradiente quase Ricci
soliton com curvatura escalar não-negativa, em que ∇ f é um campo conforme não-trivial,
é ou o espaço Euclidiano R
n ou a Esfera S
n
. Além disso, temos que no caso Esférico, a
função potencial é dada pela primeira auto função do Laplaciano. Por fim, encontraremos
condições necessárias e suficientes para que um gradiente quase Ricci soliton compacto
localmente conformemente flat seja isométrico a esfera Sn.
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Métrica produto torcido e variedades de curvatura negativa / Warped product metric and manifolds of negative curvatureSantos, Aderval Alves dos 16 April 2015 (has links)
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Previous issue date: 2015-04-16 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / This work, based on the articles M. Brozos Vazquez, E. Garcia-Rio and R. Vazquez-
Lorenzo whose goal is to build examples of manifolds locally conformally flat full of
negative curvature through warped product and multiply warped product structure. The
warped product was first introduced by Bishop and O’Neill, who modified the structure
of the Riemannian product in obtaining new manifolds of negative curvature. / Este trabalho, baseado no artigo de M. Brozos-Vázquez, E. Garcia-Río e R. Vázquez-
Lorenzo, tem como objetivo construir exemplos de variedades localmente conformemente
flat completas de curvatura negativa por meio de produto torcido e estrutura de produto
torcido mútiplo. Os produtos torcidos foram introduzidos primeiramente por Bishop e
O’Neill, que modificaram a estrutura do produto Riemanniano na obtenção de novas
variedades de curvatura negativa.
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