Inflexões de Linhas Assintóticas e de Linhas de Curvatura em Superfícies

• Autor(a) principal: FREITAS, Bruno Rodrigues de
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tde/1928
• topic: Inflexões; Linhas Assintóticas; Linhas de Curvatura; Inflections; Asymptotic Lines; Lines of Curvature; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA

Quadratic points (or special hyperbolic points) are points where a surface can be approximated by a quadric to the terms of order three. We will deal with a conjecture that asserts that every closed hyperbolic surface in RP3 has not less than eight distinct quadratic points. We prove a result which states that; if a generic surface in RP3 contains a hyperbolic disk bounded by a Jordan parabolic curve, then there is an odd number of quadratic points inside this disc. We study curves formed by the inflection points of asymptotic foliations and principals in the hyperbolic domain.We studied the behavior of the inflection curve of the asymptotically foliation near a special parabolic point (the point where the asymptotic direction is tangent to the parabolic curve), and the behavior of the inflection curve of the principal foliation near a umbilic point.