On paraquaternionic submersions of tangent bundle of order two

Abstract

In this paper we will show mainly that the canonical projection of the tangent bundle of order two,endowed with the diagonal metric,of an almost paraquaternionic Hermitian manifolds is a paraquaternionic submersion and we obtain necessarily and sufficient conditions for the total space of this projection to be paraquaternionic K\"{a}hler or locally hyper para-K\"{a}hler manifold.