@article {2014, title = {Legendre duality on hypersurfaces in K{\"a}hler manifolds}, number = {Advances in Geometry;volume 14; issue 2; pages 277-286;}, year = {2014}, publisher = {Walter de Gruyter and Co.}, abstract = {We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional K{\"a}hler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.}, doi = {10.1515/advgeom-2014-0016}, url = {http://urania.sissa.it/xmlui/handle/1963/34777}, author = {Vittorio Martino} }