2001/03/29 by Stefan Kebekus, Kebekus, Stefan · 1 citation
Mathematics · #14J45 #53C15 #53C25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14J45 #msc:53C15 #msc:53C25
paper · pdf · doi:10.48550/arxiv.math/0103208
Contains graphics. Author-supplied PDF-file with hyperlinks can be found at http://btm8x5.mat.uni-bayreuth.de/~kebekus
arxiv created 2001/03/29 · openalex publication_date 2001/03/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Complex contact manifolds have recently received considerable attention. Many of the newer publications approach contact manifolds via the covering family of minimal rational curves. This short note furthers the study of these curves. It is known that for any point x in X, the subvariety, which is covered by those curves which contain x, is Legendrian. We will now study the deformations of these subvarieties which are generated by moving the base point. As a main application, we give a positive answer to a question of J.M. Hwang in the case of contact manifolds: a sufficiently general tangent vector is contained in at most a single minimal rational curve. The author believes that this is a necessary step towards a full classification of contact manifolds. We give a second application by showing that the normalization of the subvariety of minimal curves through x is isomorphic to a projective cone.