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Previous issue date: 2009-03-13 / language="eng">The present work has been based by the [16] and [17] articles, from Oscar J. Garay. In
that articles he studied the conformally flat hypersurfaces in the R4 space, wich have the
mean curvature vector H like an eigenvector of their Laplacian Operator, i.e., DH = lH,
l 2R .We showed that these hypersurfaces are isoparametrics and, consequently, they are
either a minimal hypersurface, or an around 3-sphere S3(r) , or a cylinder over a 2-sphere
S2(r) R, or a cylinder over a circle S(r) R2. / Este trabalho foi baseado nos artigos [16] e [17] de Oscar J. Garay que consistem em
estudar as hipersuperfícies conformemente planas em R4, cujo vetor curvatura média,
H, ´e autovetor do operador Laplaciano, isto ´e, DH = lH, com l 2 R. Mostramos que
estas hipersuperfícies são isoparamétricas e, consequentemente, são m´ınimas, ou uma
hiperesfera S3(r), ou um cilindro cartesiano com uma 1-esfera R2 S1(r), ou um cilindro
cartesiano com uma 2-esfera R S2(r).
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tde/2905 |
| Date | 13 March 2009 |
| Creators | Moreira, Lucas |
| Contributors | Pina, Romildo da Silva |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em Matemática (IME), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
| Relation | 6600717948137941247, 600, 600, 600, -4268777512335152015, -7090823417984401694 |
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