Contato e vertices de curvas em variedades de curvatura constante

AUTOR(ES)

Claudia Candida Pansonato

DATA DE PUBLICAÇÃO

2001

RESUMO

In this work some concepts and results relating higher order singularities and curve contact with curves and sub manifolds are extended to constant curvature manifolds. This is an intrinsic Riemannian approach to curvatures, vertices and contact via conformal parameterizations. The vertex characterization considered here generalizes the Euclidean notion of higher order contact with the osculating circle. The results here include relations between the vanishing of Riemannian curvatures of a curve and its contact with totally geodesic submanifolds and the statement that Riemannian vertices are correspondent to the Euclidean ones via conformal parametrization if and only if the manifold is of constant curvature. As a consequence a four-vertex theorem for spherical curve on constant curvature manifold is proved. It is also shown some specific statements for three dimensional manifolds like a characterization of vertices as cuspidal edges of the conformal pre-image evolute surface and a Riemannian extension of the total torsion theorem for spherical curves

ASSUNTO(S)

singularidades (matematica) curvatura curvas

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