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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2018.tde-18012018-152530
Document
Author
Full name
Euripedes Carvalho da Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Gomes, André de Oliveira (President)
Almeida, Sebastiao Carneiro de
Brito, Fabiano Gustavo Braga
Silva, Márcio Fabiano da
Silva, Marcos Martins Alexandrino da
Title in Portuguese
Folheações ortogonais em variedades riemannianas
Keywords in Portuguese
Folheação totalmente umbílica
Fórmula integra
Vetor curvatura média
Abstract in Portuguese
Neste trabalho, estabelecemos uma equação que relaciona a curvatura de Ricci de uma variedade riemanniana M e as segundas formas fundamentais de duas folheações ortogonais de dimensões complementares, F e F, definidas em M. Usando essa equação, encontramos uma estimativa da curvatura média da folheação F e uma condição necessária e suficiente para que tal folheação seja totalmente geodésica. Mostramos também uma condição suficiente para que M seja localmente um produto riemanniano das folhas de F e F, se uma das folheações for totalmente umbílica. Por fim, provamos ainda uma fórmula integral válida para tais folheações.
Title in English
Orthogonal foliations on riemannian manifolds
Keywords in English
Integral formula
Mean curvature vector
Totally umbilical foliation
Abstract in English
In this work, we and an equation that relates the Ricci curvature of a riemannian manifold M and the second fundamental forms of two orthogonal foliations of complementary dimensions, F and F, defined on M. Using this equation, we and an estimate of the mean curvature of the foliation F and a necessary and suficient condition for the foliation F to be totally geodesic. We also show a suficient condition for the manifold M to be locally a riemannian product of the leaves of F and F, if one of the foliations is totally umbilical. Finally, we also prove an integral formula for such foliations.
 
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euripedes.pdf (415.99 Kbytes)
Publishing Date
2018-02-08
 
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