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Advisor(s)
Abstract(s)
Fazendo uso da projeção isotrópica para a geometria de Laguerre, estabelecemos uma correspondência entre curvas do tipo luz no espaço tridimensional de Minkowski e curvas no plano euclidiano. Descrevemos a geometria das curvas do tipo luz (triedro de Frenet-Serret, pseudo-comprimento de arco, pseudo-torção, pares de curvas associadas) em termos da curvatura das curvas planas correspondentes. Isto irá conduzir-nos a uma caracterização original de todas as curvas planas que são Laguerre-congruentes com uma curva dada.
We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski 3-space. We describe the geometry of null curves (Frenet-Serret frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the corresponding plane curves. This leads to an alternative description of all plane curves which are Laguerre congruent to a given one.
We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski 3-space. We describe the geometry of null curves (Frenet-Serret frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the corresponding plane curves. This leads to an alternative description of all plane curves which are Laguerre congruent to a given one.
Description
Keywords
Geometria diferencial de curvão