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We investigate the geometry of Legendrian complex projective manifolds X ⊂ ℙV. 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.
author list (cited authors)
Landsberg, J. M., & Manivel, L.