dc.contributor | Figueiredo Junior, Ruy Tojeiro de | |
dc.contributor | http://lattes.cnpq.br/9930999514347198 | |
dc.contributor | http://lattes.cnpq.br/3520357439188664 | |
dc.creator | Guimarães, Daniel da Silveira | |
dc.date.accessioned | 2016-09-30T14:04:28Z | |
dc.date.available | 2016-09-30T14:04:28Z | |
dc.date.created | 2016-09-30T14:04:28Z | |
dc.date.issued | 2015-06-09 | |
dc.identifier | GUIMARÃES, 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.identifier | https://repositorio.ufscar.br/handle/ufscar/7583 | |
dc.description.abstract | In 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.language | por | |
dc.publisher | Universidade Federal de São Carlos | |
dc.publisher | UFSCar | |
dc.publisher | Programa de Pós-Graduação em Matemática - PPGM | |
dc.publisher | Câmpus São Carlos | |
dc.rights | Acesso aberto | |
dc.subject | Geometria diferencial | |
dc.subject | Transformação de Ribaucour | |
dc.subject | Espaços de curvatura constante | |
dc.subject | Subvariedade Lagrangiana | |
dc.subject | Imersão isométrica horizontal | |
dc.title | A transformação vetorial de Ribaucour para subvariedades de curvatura constante | |
dc.type | Tesis | |