Structures Symplectiques sur les Espaces de Courbes Projectives et Affines

Abstract

A symplectic structure on the space of nondegenerate and nonparametrized curves in a locally affine manifold is defined. We also consider several interesting spaces of nondegenerate projective curves endowed with Poisson structures. This construction connects the Virasoro algebra and the Gel'fand-Dikii bracket with the projective differential geometry.