Generalization of Wente torus in complex spaces forms

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Parallel mean curvature vector surfaces in complex space forms are studied. It is proved that, when the codimension of the immersion is two, the set of such surfaces is divided in two families, which are called cmc type and general type. The surface of cmc type depends on one real valued harmonic function and the one of general type, if it exists, depends on two independent real valued functions. Related to the theory of constant mean curvature surfaces, we studied also rotational surfaces with periodic mean curvature. In order to extend the research to higher dimension, we proved the existence theorem of rotational hypersurfaces with prescribed mean curvature function.