Legacy of Jorge Sotomayor

This paper is a tribute to Jorge Sotomayor. He was a mathematician with pioneering contributions to bifurcations of ode’s and the qualitative theory (stability and bifurcations) of principal curvature lines. These themes are developed in the Sections 3 and 4. He had a great capacity for synthesis, a keen intuition, and an exceptional ability to make sketches of bifurcation diagrams and phase portraits of vector fields and principal lines (true works of modern art). Influenced by Peixoto’s theorem, he founded the qualitative theory of principal lines on surfaces, and together with C. Gutiérrez they published their seminal works in 1982 and 1983.