Imersões isométricas em produtos de duas formas espaciais

• Autor(a) principal: Santos, Bruno Mendonça Rey dos
• Data de Publicação: 2012
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5825
• topic: Geometria; Imersões isométricas; Variedades diferenciáveis; Espaços de curvatura constante; Subvariedades umbílicas; Subvariedades paralelas; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this thesis we study isometric immersions into products of two space forms using the approach introduced by Lira et al in [18]. Parallel isometric immersions into products of two space forms with nonzero sectional curvatures are classified, and the classification of umbilical isometric immersions f : Mm Ñ On1 k1 _ On2 k2 , with m ¥ 3 and k1 􀀀 k2 _ 0, is reduced to that of umbilical isometric immersions of codimension two into On k _ R, k 0, where On k denotes the space form with dimension n and sectional curvature k. To accomplish this, we prove some results of independent interest on reduction of codimension of isometric immersions into products of two space forms.