As we know contact manifolds have odd dimension and K\"ahler are even. In this point of view I think this not possible. But underlying manifold colud be K\"ahler. If your answer is yes, what woluld be a relation between contact form and K\"ahler form?
Dear Prof. Robert J. Low thank you for your answer. In complex contact geometry there two definitions for normality which one is an extension other and under one of these normality conditions the underlying manifold is K\"ahler. So I try to understand the relation between these two structure.
Since a holomorphic p-form on compact Kahler manifold is closed, no compact Kahler manifold had a complex contact structure given by a global contact form, this is proved by Goldberg in 1962.
Dear, Saeed nazari nezhad thank you for your answer. I also know this result. For globality of complex contact form the first Chern class of manifold must be zero. Under normality (Ishihara-Konishi) the first Chern class is positive and manifold K\"ahler Einstein. So these type of normality has not global complex contact form. What we could consider about non-compact case?
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