2000/04/16 by Stefan Kebekus, Kebekus, Stefan
Mathematics · #53C15 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Primary 53C25 #Secondary 14J45 #math.AG #math.DG #msc:14J45 #msc:53C15 #msc:53C25
paper · pdf · doi:10.48550/arxiv.math/0004103
reason for resubmission: improved exposition
openalex publication_date 2000/04/16 · arxiv created 2000/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a complex Fano-manifolds with second Betti-number 1 which carries a contact structure. It follows from previous work that such a manifold can always be covered by lines. Thus, it seems natural to consider the geometry of lines in greater detail. In this brief note we show that if x in X is a general point, then all lines through x are smooth. If X is not the projective space, then the tangent spaces to lines generate the contact distribution at x. As a consequence we obtain that the contact structure on X is unique, a result previously obtained by C. LeBrun in the case that X is a twistor space.