Almost para-Hermitian submersions

Abstract

In this paper, we introduce theconcept of almost para-Hermitian submersions between almostpara-Hermitian manifolds. We investigate the influence of a givenstructure defined on the total manifold on the determination of thecorresponding structure on the base manifold. Moreover, we providean example, investigate various properties of the O'Neill's tensorsfor such submersions, find the integrability of the horizontaldistribution and obtain necessary and sufficient conditions for thefibres of an almost para-Hermitian submersion to be totallygeodesic. We also obtain curvature relations between the basemanifold and the total manifold.