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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2020.tde-21122020-155111
Document
Author
Full name
Leonardo Francisco Cavenaghi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Sperança, Llohann Dallagnol (President)
Bettiol, Renato Ghini
Caramello Junior, Francisco Carlos
Melo, Mateus Moreira de
Radeschi, Marco
Title in Portuguese
Deformações métricas e aplicações
Keywords in Portuguese
Curvatura escalar prescrita
Curvatura não-negativa
Curvatura positiva
Deformações métricas
Fluxo de curvatura média
Variedades exóticas
Abstract in Portuguese
Nesta tese estudamos diversas deformações métricas com o intuito de construir novos exemplos e encontrar condições necessárias e suficientes para existência de métricas com propriedades de curvatura (não-negativa e positiva), possivelmente construindo novos exemplos, sendo esses baseados em variedades exóticas. Estudamos também o comportamento limite de fluxos de curvatura média em variedades com folheações riemannianas singulares além do problema de prescrever curvatura escalar em grandes classes de fibrados.
Title in English
On metric deformations and applications
Keywords in English
Exotic manifolds
Mean Curvature Flow
Metric deformations
Non-negative/positive curvatures
Prescribing scalar curvature
Abstract in English
In this thesis we study several metric deformations in order to build new examples and find necessary and sufficient conditions for the existence of metrics with curvature properties (non-negative and positive), possibly building new examples, which are based on exotic manifolds. We also studied the limit behavior of the Mean Curvature Flow on manifolds with Singular Riemannian foliations, in addition to the problem of prescribing scalar curvature in large classes of bundles.
 
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Publishing Date
2021-01-20
 
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