Inflection points and asymptotic lines on Lagrangian surfaces

Abstract

We describe the structure of the asymptotic lines near an inflection point of a Lagrangean surface, proving that in the generic situation it corresponds to two of the three possible cases when the discriminant curve has a cusp singularity. Besides being stable in general, inflection points are proved to exist on a compact Lagrangean surface whenever its Euler characteristic does not vanish.