Date/heure
12 janvier 2016
14:00 - 15:00
Oratrice ou orateur
Joà£o Paulo dos Santos
Catégorie d'évènement Séminaire de géométrie différentielle
Résumé
It is known that conformally flat hypersurfaces in four dimensional space forms are associated with solutions of a system of equations, known as Lam ́eâs system. In this talk, conformally flat hypersurfaces associated with invariant solutions under the symmetry group of the Lam ́eâs system are considered. Namely, three classes of solutions are presented: a) solutions given by Jacobi elliptic functions, that correspond to a new class of conformally flat hypersurfaces; b) solutions given by hyperbolic functions, that correspond to conformally flat hypersurfaces generated by helicoidal flat surfaces in the hyperbolic three space; c) solutions given by trigonometric functions, that correspond to conformally flat hypersurfaces generated by helicoidal flat surfaces in the standard three sphere. For such helicoidal flat surfaces, a classification is given in terms of their first and second fundamental forms for special parametrizations.