Espaces projectifs : Structures additionnelles sur un espace projectif

Abstract

Our work is devoted to the analysis of a new geometric space in which all the straight lines are secant : the projective space. We use vectorial and affine spaces properties to have the following results : - A projective space is an affine space completed by some points called infinity points. -A projective space, except an hyperplane, has an affine space structure. -PAPPUS and DESARGUES theorems have simplified terms and demonstrations in a projective space. -In a complex projective space we also have a structure which let reals points invariant. -In a projective space, we also have the notion of angle between two straight lines