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A connected Fano complex-contact manifold is isomorphic to the kaehlerianC-space of Boothby type with a natural complex-contact structure correspondingto a non-abelian simple complex Lie algebra if the contact line bundle is veryample. A. Beauville relaxed the provision to two assumptions that the contactline bundle is generically finite and that the automorphism group is reductive.We relax the provision to another one that that the contact line bundle isimmersive, that is, the manifold admits a holomorphic immersion into someprojective space associated with some holomorphic sections of the line bundle.As an application, we obtain that the automorphism group of a connected compactcomplex-contact manifold with immersive contact line bundle is isomorphic tothe automorphism group of the corresponding simple complex Lie algebra of rankgreater than one, which is not connected if and only if its type is A_{n},D_{n+2} for n > 1 or E_{6}.

Immersivity of the contact line bundle of a complex-contact manifold and an application to the automorphism group