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We describe the structure of the asymptotic lines near an inflection point ofa Lagrangean surface, proving that in the generic situation it corresponds totwo of the three possible cases when the discriminant curve has a cuspsingularity. Besides being stable in general, inflection points are proved toexist on a compact Lagrangean surface whenever its Euler characteristic doesnot vanish.

Inflection points and asymptotic lines on Lagrangean surfaces