General helices and a theorem of Lancret

1997/05/01 by Manuel Barros · 19 citations
Mathematics · Computer Science · #Mathematics and Applications #Geometric Analysis and Curvature Flows #Computational Geometry and Mesh Generation

paper · doi:10.1090/s0002-9939-97-03692-7

Abstract

We present a theorem of Lancret for general helices in a 3-dimen- sional real-space-form which gives a relevant difference between hyperbolic and spherical geometries. Then we study two classical problems for general helices in the 3-sphere: the problem of <italic>solving natural equations</italic> and the <italic>closed curve</italic> problem.

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