An Obata-type characterization of doubly-warped product Kahler manifolds

We give a characterization a` la Obata for certain families of Kahler manifolds. These results are in the same line as other extensions of the well-known Obata rigidity theorem from [16], like for instance the generalizations in [17, 18]. Moreover, we give a complete description of the so-called Kahler doubly-warped product structures whose underlying metric is Einstein.