Uniqueness of complex contact structures
Abstract
Let X be a complex Fanomanifolds with second Bettinumber 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2000
 arXiv:
 arXiv:math/0004103
 Bibcode:
 2000math......4103K
 Keywords:

 Algebraic Geometry;
 Differential Geometry;
 Primary 53C25;
 Secondary 14J45;
 53C15
 EPrint:
 reason for resubmission: improved exposition