Abstract

We shall construct \emph{complex contact similarity manifolds}. Among them there exists a complex contact infranilmanifold $\cL/\Gamma$ which is a holomorphic torus fiber space over a  quaternionic euclidean orbifold. Specifically taking a connected sum of $\cL/\Gamma$ with the complex projective space $\CC\PP^{2n+1}$, we prove that the connected sum admits a complex contact structure. Our examples of complex contact manifolds  are different from those known previously as complex Boothby-Wang fibration (Foreman, 2000) or the twistor fibration (Salamon, 1989).

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