Teorema de Schur no plano de Minkowski e caracterização de hélices inclinadas no espaço de Minkowski
Ramos, Luciano de Melo
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A classical theorem of differential geometry of curves in Euclidean space is the Schur's Theorem, that was proof by A. Schur in 1921, when both curvatures agree pointwise . The proof in the general case was proved in 1925 by E. Schmidt in . The first objective in this dissertation is to present Lorentzian version of Schur's Theorem in the Minkowski plane. Then we will show some applications due to R. López . In the Minkowski space we will see that the Schur's Theorem is false. The second objective is show a characterization of slant helices in the Minkowski space obtained by A. T. Ali and R. López in , which extends naturally a characterization of slant helices in Euclidean space obtained in 2004 by S. Izumiya And N. Takeuchi . We conclude with an application that characterization of slant helices .