The present work is concerned with the study of complex projective manifolds X which carry a complex contact structure. In the first part of the paper we show that if K X is not nef, then either X is Fano and b 2(X)=1, or X is of the form ℙ(T Y ), where Y is a projective manifold. In the second part of the paper we consider contact manifolds where K X is nef.
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