Legendrian varieties

By J. M. Landsberg, Laurent Manivel. 2004

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. We investigate the geometry of Legendrian complex projective manifolds X ⊂ P V . By definition, this means V is a complex vector space of dimension 2 n + 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.

Subfields: Applied Mathematics, Geometry and Topology

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