Para-Kaehler immersions in para-Kaehler space forms

Abstract

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