Almost para-Hermitian submersions. (English) Zbl 1474.53150

Summary: In this paper, we introduce the concept of almost para-Hermitian submersions between almost para-Hermitian manifolds. We investigate the influence of a given structure defined on the total manifold on the determination of the corresponding structure on the base manifold. Moreover, we provide an example, investigate various properties of the O’Neill’s tensors for such submersions, find the integrability of the horizontal distribution and obtain necessary and sufficient conditions for the fibres of an almost para-Hermitian submersion to be totally geodesic. We also obtain curvature relations between the base manifold and the total manifold.


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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