Vari\'{e}t\'{e}s de type Togliatti

The Del Pezzo surface S_6 obtained by blowing up the projective plane along three points (non aligned) has the following nice property : its osculating hyperplanes have a common point. For that reason S_6 is also called Togliatti surface. In this paper we give two explanations of this fact. After what we obtain two different families of varieties with an analogous property.