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11 
Eine Riemannsche Betrachtung des ReebFlussesHainz, Stefan. January 2006 (has links)
Thesis (doctoral)Rheinische FriedrichWilhelmsUniversität Bonn, 2006 / Includes bibliographical references (p. 5960).

12 
Riemannian geometry of compact metric spacesPalmer, Ian Christian 21 May 2010 (has links)
A construction is given for which the Hausdorﬀ measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorﬀ measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorﬀ and box dimensions diﬀerin particular, it does not depend on any selfsimilarity or regularity conditions on the space. The only restriction on the space is that it have positive s₀ dimensional Hausdorﬀ measure, where s₀ is the Hausdorﬀ dimension of the
space, assumed to be ﬁnite. Also, X does not need to be embedded in another space, such as Rⁿ.

13 
Weierstrass points and canonical cell decompositions of the moduli and teichmüller spaces of riemann surfaces of genus two /Rodado A., Armando J. January 2007 (has links)
Thesis (Ph.D.)University of Melbourne, Dept. of Mathematics and Statistics, 2007. / Typescript. Includes bibliographical references.

14 
The noncommutative geometry of ultrametric cantor setsPearson, John Clifford January 2008 (has links)
Thesis (Ph.D.)Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Bellissard, Jean; Committee Member: Baker, Matt; Committee Member: Bakhtin, Yuri; Committee Member: Garoufalidis, Stavros; Committee Member: Putnam, Ian

15 
Ricci YangMills FlowStreets, Jeffrey D., January 2007 (has links)
Thesis (Ph. D.)Duke University, 2007. / Includes bibliographical references.

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Nodal sets and contact structuresKomendarczyk, Rafal. January 2006 (has links)
Thesis (Ph. D.)Mathematics, Georgia Institute of Technology, 2007. / Belegradek, Igor, Committee Member ; Ghrist, Robert, Committee Chair ; Harrell, Evans, Committee Member ; Etnyre, John, Committee Member ; Symington, Margaret, Committee CoChair.

17 
Solution generating algorithms in general relativity.Krupanandan, Daniel D. January 2011 (has links)
We conduct a comprehensive investigative review of solution generating algorithms
for the Einstein field equations governing the gravitational behaviour of an isolated
neutral static spherical distribution of perfect fluid matter. Traditionally, the master
field equation generated from the condition of pressure isotropy has been interpreted
as a second order ordinary differential equation. However, since the pioneering work
of Wyman (1949) it was observed that more success can be enjoyed by regarding
the equation as a first order linear differential equation. There was a resurgence
of the ideas of Wyman in 2000 and various researchers have been able to generate
complete solutions to the field equations up to certain integrations. These have
been accomplished by working in Schwarzschild (curvature) coordinates, isotropic
coordinates, area coordinates and a coordinate system written in terms of the redshift
parameter. We have utilised Durgapal–Banerjee (1983) coordinates and produced a
new algorithm. The algorithm is used to generate new classes of perfect fluid solutions
as well as to regain familiar particular solutions reported in the literature. We find
that our solution is well behaved according to elementary physical requirements.
The pressure vanishes for a certain radius and this establishes the boundary of the
distribution. Additionally the pressure and energy density are both positive inside
the radius. The energy conditions are shown to be satisfied and it is particularly
pleasing to have the causality criterion satisfied to ensure that the speed of light is
not exceeded by the speed of sound. We also report some new solutions using the
algorithms proposed by Lake (2006). / Thesis (M.Sc.)University of KwaZuluNatal, Westville, 2011.

18 
Modificações do tensor de Ricci e aplicações / Modifications of the Ricci tensor and applicationsYalanda Muelas, Yamit Yesid, 1988 21 August 2018 (has links)
Orientador: Diego Sebastian Ledesma / Dissertação (mestrado)  Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 20180821T14:31:48Z (GMT). No. of bitstreams: 1
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Previous issue date: 2012 / Resumo: Nesta dissertação apresentamos generalizações de três resultados muito conhecidos em geometria Riemanniana: o Teorema de Myers, o Teorema de Bochner e o Teorema de decomposição de CheegerGromoll. Em particular veremos que fazendo uma pequena modificação sobre os requisitos destes teoremas no que se refere ao tensor de Ricci, os resultados permanecem inalterados / Abstract: In this dissertation we present generalizations of three wellknown results in Riemannian geometry: The Myers's theorem, Bochner's theorem and the CheegerGromoll splitting theorem. In particular, we will prove that making a small modification of the requirements of these theorems related to the Ricci tensor, the results remain unchanged / Mestrado / Matematica / Mestre em Matemática

19 
Consequências geométricas associadas à limitação do tensor de BakryÉmeryRicci / Geometric consequences associated to the limitation of the BakryÉmeryRicci tensorPaula, Pedro Manfrim Magalhães de, 1991 26 August 2018 (has links)
Orientador: Diego Sebastian Ledesma / Dissertação (mestrado)  Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 20180826T22:36:25Z (GMT). No. of bitstreams: 1
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Previous issue date: 2015 / Resumo: Este trabalho apresenta um estudo sobre variedades Riemannianas que possuem um tensor de BakryÉmeryRicci com limitações. Inicialmente abordamos tanto aspectos da geometria Riemanniana tradicional como métricas e geodésicas, quanto aspectos mais avançados como as fórmulas de Bochner, Weitzenböck e o teorema de Hodge. Em seguida discutimos a convergência de GromovHausdorff e suas propriedades, além de serem apresentados alguns teoremas como os de Kasue e Fukaya. Por fim estudamos as propriedades topológicas e geométricas de variedades com limitação no tensor de BakryÉmeryRicci e o comportamento de tais limitações com respeito à submersões e à convergência de GromovHausdorff / Abstract: This work presents a study about Riemannian manifolds having a BakryÉmeryRicci tensor with bounds. Initially we approached both the traditional aspects of Riemannian geometry like metrics and geodesics, as more advanced aspects like the Bochner, Weitzenböck formulas and the Hodge's theorem. Then we discussed the GromovHausdorff convergence and its properties, in addition to showing some theorems as those from Kasue and Fukaya. Lastly we studied the topological and geometric properties of manifolds with bounds on the BakryÉmeryRicci tensor and the behavior of these bounds with respect to submersions and the GromovHausdorff convergence / Mestrado / Matematica / Mestre em Matemática

20 
Ações e folheações polares em variedades de HadamardCaramello Junior, Francisco Carlos 27 February 2014 (has links)
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Previous issue date: 20140227 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O objetivo principal deste trabalho é apresentar alguns resultados recentes na teoria de folheações polares, também chamadas de folheações riemannianas singulares com seções, em variedades de curvatura não positiva, presentes no artigo [24]. As ações polares também são estudadas, pois são objetos de pesquisa ativa que motivam e ilustram o estudo das folheações polares. Fornecemos uma demonstração de que não existem folheações polares próprias em variedades compactas de curvatura não positiva. Além disso, apresentamos um resultado que descreve globalmente as folheações polares próprias em variedades de Hadamard. Abordamos este resultado também no contexto particular das ações polares, utilizando a teoria de subvariedades taut. As ações adjunta e por conjugação são brevemente estudadas como exemplos clássicos de ações polares. / This work aims at presenting some recent results on the theory of polar foliations, also know as singular riemannian foliations with sections, on nonpositively curved manifolds, as seen in T oben [24]. Polar actions are also studied, for they are active research subject that motivate and illustrate polar foliations. We give a proof of the nonexistence of proper polar foliations on compact manifolds of nonpositive curvature. Then we present a result that globally describes proper polar foliations on Hadamard manifolds. We prove this same result in the special case of polar actions by using the theory of taut submanifolds. The adjoint and conjugation actions are brie y presented as classical examples of polar actions.

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