Geodésicas em superfícies poliedrais e elipsóides

• Autor(a) principal: Plaza, Luis Felipe Narvaez
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6216
• topic: Geodésica; Superfícies poliedrais; Elipsóide; Geodesics; Polyhedral surfaces; Ellipsoids; GEOMETRIA E TOPOLOGIA::SISTEMAS DINAMICOS

This work is divided in four parts, in the first chapter we give an introduction. In the next chapter we study basic theory of geometry and differential equations, we study some results of geodesics theory on surfaces in R3; based in the works of R. Garcia and J. Sotomayor in [10] and W. Klingenberg in [15]. These ones provide a study of the behavior of the geodesic in the ellipsoid. The third chapter is inspired by the famous question given in 1905, in his famous article “Sur les lignes géodésiques des surfaces convexes” H. Poincaré posed a question on the existence of at least three geometrically different closed geodesics without self-intersections on any smooth convex two-dimensional surface (2-surface) M homeomorphic to the two-dimensional sphere (2-sphere) S2. We study this question for convex polyhedral surfaces following the paper [9] by G. Galperin and the books [1],[4]. In the last topic we will address the behavior of geodesics on Lorentz surfaces, focusing our study on the ellipsoid based mainly on the book of Tilla Weinstein [25] and in the paper [11] by S. Tabachnikov, Khesin and Genin.