Remarks on complex contact manifolds

  title={Remarks on complex contact manifolds},
  author={Sh{\^o}shichi Kobayashi},
1. Statement of results. Let M be a complex manifold of complex dimension 2n+1. Let { Ui} be an open covering of M. We call M a complex contact manifold if the following conditions are satisfied: (1) On each Ui there exists a holomorphic 1-form coi such that ciA(dci)" is different from zero at every point of U;. (2) If U,\ Us is nonempty, then there exists a nonvanishing holomorphic function f;q on U;C US such that cow =f,wj on Ui; Us. We shall prove the following 

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