Ciclos principais hiperbólicos em hipersuperfícies do R4

• Autor(a) principal: Cruz, Dayane Ribeiro
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: https://ri.ufs.br/handle/riufs/5792
• topic: Matemática; Superfícies (Matemática); Hipersuperfícies; Séries de Poincaré; Espaços hiperbólicos; Curvatura; Linha de curvatura; Ciclo principal hiperbólico; Hipersuperfície; Mapa de primeiro retorno de Poincaré; Curvature line; Home cycle hyperbolic; Hypersurface first return Poincaré map; CIENCIAS EXATAS E DA TERRA::MATEMATICA

Based on the article “Hyperbolic Main Cycles on Hypersurface of R4”, Garcia, see [4], we will study the bending lines in the vicinity of a main loop, closed bending line, a hypersurface immersed in R4. For this, we will define the Poincaré transformation associated with the cycle and calculate its derivative. With this analysis, we show under what conditions we can become hyperbolic, with a small deformation in the immersion, a major cycle given. Finally, we will build an example of a hypersurface containing a hyperbolic primary cycle, based on the article “Surfaces Around Closed Main Curvature Lines, an Inverse Problem." Garcia, Mello and Sotomayor, see [5].