Para-Quaternionic Structures on the 3-Jet Bundle

Abstract

In this paper we construct an almost para-quaternionic structure on the 3-jet bundle of an almost parahermitian manifold and we study its integrability. We give a necessary and sufficient conditions that are provided for these structures to become para-hyper-Kähler and we prove that the 3-jet bundle can not be a para-quaternionic Kähler manifold.