Structural stability of asymptotic lines on surfaces immersed in R-3

In this paper are studied immersions of surfaces into to R-3 whose nets of asymptotic lines are topologically undisturbed under small perturbations of the immersion. These immersions are called structurally asymptotic stable. Sufficient conditions to belong to this class are established here. These conditions focus on the stable patterns around parabolic points, parabolic separatrix connections, periodic asymptotic lines (including those that int ercept the parabolic lines) as well the exclusion of recurrent asymptotic l ines. The class of immersions that are structurally stable in this sense is open in the C-5-topology. (C) Editions scientifiques et medicales Elsevier SAS.