Para-Kaehler immersions in para-Kaehler space forms

In this paper, we provide necessary and sufficient conditions for the existence of para-K¨ahler immersions in para-K¨ahler space forms. As a consequence, we prove that, in general, a local para-K¨ahler immersion cannot be globally extended, even if it is defined on a simply connected para-K¨ahler manifold. Finally, we classify para-K¨ahler immersions between para-K¨ahler space forms.