We investigate the geometry of Legendrian complex projective manifolds X V. By definition, this means V is a complex vector space of dimension 2n + 2, endowed with a symplectic form, and the affine tangent space to X at each point is a maximal isotropic subspace. We establish basic facts about their geometry and exhibit examples of inhomogeneous smooth Legendrian varieties, the first examples of such in dimension greater than one. 2007 International Press.
