dc.contributorFigueiredo Junior, Ruy Tojeiro de
dc.contributorhttp://lattes.cnpq.br/9930999514347198
dc.contributorhttp://lattes.cnpq.br/3520357439188664
dc.creatorGuimarães, Daniel da Silveira
dc.date.accessioned2016-09-30T14:04:28Z
dc.date.available2016-09-30T14:04:28Z
dc.date.created2016-09-30T14:04:28Z
dc.date.issued2015-06-09
dc.identifierGUIMARÃES, Daniel da Silveira. A transformação vetorial de Ribaucour para subvariedades de curvatura constante. 2015. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2015. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7583.
dc.identifierhttps://repositorio.ufscar.br/handle/ufscar/7583
dc.description.abstractIn this work we obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds with constant sectional curvature of space forms. As a consequence, a process is derived to generate a new family of such submanifolds starting from a given one. We prove a decomposition theorem for this transformation, from which the classical permutability theorem for the Ribaucour transformation of submanifolds with constant sectional curvature follows. Given k scalar Ribaucour transforms of a submanifold with constant sectional curvature, we prove the existence of a Bianchi k-cube all of whose vertices are submanifolds with the same constant sectional curvature, each of which is given by means of explicit algebraic formulas. A further reduction of the transformation is shown to preserve the class of Lagrangian submanifolds of dimension n and constant sectional curvature c of complex space forms of complex dimension n and constant holomorphic sectional curvature 4c. In particular, explicit parametrizations in terms of elementary functions of examples with arbitrary dimension and curvature are provided. A decomposition theorem and a version of the Bianchi cube for this transformation are also obtained.
dc.languagepor
dc.publisherUniversidade Federal de São Carlos
dc.publisherUFSCar
dc.publisherPrograma de Pós-Graduação em Matemática - PPGM
dc.publisherCâmpus São Carlos
dc.rightsAcesso aberto
dc.subjectGeometria diferencial
dc.subjectTransformação de Ribaucour
dc.subjectEspaços de curvatura constante
dc.subjectSubvariedade Lagrangiana
dc.subjectImersão isométrica horizontal
dc.titleA transformação vetorial de Ribaucour para subvariedades de curvatura constante
dc.typeTesis


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