Linhas assintóticas de campos de planos em R3 e de superfícies em R4 - Cruz, Douglas Hilário da (2017)
This work is divided into two parts. The first part deals with asymptotic lines of plane fields in R3. The main results are the analysis of the asymptotic lines in a neighborhood of the regular surface of parabolic points and the analysis of the stability of closed asymptotic lines. We express the first derivative of the Poincar\'e map and show how to make hyperbolic a closed asymptotic line. The second part deals with asymptotic lines of surfaces in R4. The main results are results of structural stability and genericity for asymptotic lines of locally convex surfaces in R4 and a result of structural stability asymptotic lines of surfaces in R4.