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Lines of curvature near umbilical points on surfaces immersed in R4
Authors:Federico Sánchez-Bringas  Ana Irene Ramírez-Galarza
Affiliation:(1) Departmento de Matemáticas Facultad de Ciencias, U.N.A.M., 04510 México, D.F., México
Abstract:LetM be a compact orientable surface,I:M rarr R4 an immersion of classCr and
$$widehat{v}$$
a normal unitary smooth vector field. We prove that in the space of pairs (I,
$$widehat{v}$$
) the family of pairs all whose umbilical points are Darbouxian is generic.
Keywords:Principal configurations  structural stability  umbilical points
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