Palestra Especial

A lecture evocative of the memory of Carlos Gutierrez and his mathematical contributions on Principal Curvature Configurations and Umbilic Points on Euclidean Surfaces. Very brief time line of Carlos Gutierrez career, centered around 1981, date of the lecture on the Structurally Stable Principal Curvature Configurations on Surfaces, at the International Dynamical Systems Conference on the occasion of IMPA's new building inauguration. Mathematical and historical landmarks, with references, leading to the results presented in the above 1981 lecture. Extensions to higher dimensions of the study on principal curvature configurations and their umbilic singularities and the discussion of some open old and present day problems .