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Doctoral Thesis
DOI
10.11606/T.45.2013.tde-07112013-142031
Document
Author
Full name
Juan Fernando Zapata Zapata
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Asperti, Antonio Carlos (President)
Lymberopoulos, Alexandre
Sousa Junior, Luiz Amancio Machado de
Vilhena, José Antônio Moraes
Villagra, Guillermo Antonio Lobos
Title in Portuguese
Hipersuperficies completas com curvatura de Gauss-Kronecker nula em esferas
Keywords in Portuguese
curvatura de Gauss-Kronecker
cuvaturatura media constante
Hipersuperfícies
Abstract in Portuguese
Neste trabalho mostramos que hipersuperfícies completas da esfera Euclidiana S^4, com curvatura média constante e curvatura de Gauss-Kronecker nula são mínimas, sempre que o quadrado da norma da segunda forma fundamental for limitado superiormente. Além disso apresentamos uma descrisão local das hipersuperfícies mínimas e completas em S^5 com curvatura de Gauss- Kronecker nula e algumas hipóteses adicionais sobre as funções simétricas das curvaturas principais.
Title in English
Complete hypersurfaces with constant mean curvature and zero Gauss-Kronecker curvature in spheres.
Keywords in English
Complete hypersurfaces
constant mean curvature.
Gauss-Kronecker curvature
minimal hypersurfaces
Abstract in English
In this work we show that a complete hipersurface of the unitary sphere S^4, with constant mean curvature and zero Gauss-Kronecker curvature must be minimal, if the squared norm of the second fundamental form is bounded from above. Also, we present a local description for complete minimal hipersurfaces in S^5 with zero Gauss-Kronecker curvature, and some restrictions for the symmetric functions of the principal curvatures.
 
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tese.pdf (396.75 Kbytes)
Publishing Date
2013-11-08
 
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