Geodésicas em superfícies poliedrais e elipsóides
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2016-03-14
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Universidade Federal de Goiás
Resumo
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.
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PLAZA, L. F. N. Geodésicas em superfícies poliedrais e elipsóides. 2016. 93 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás,Goiânia, 2016.