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The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in complex space forms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce semi-invariant semi-Riemannian submersions from para-Kähler manifolds onto semi-Riemannian manifolds. We give some examples, investigate the geometry of foliations that arise from the definition of a semi-Riemannian submersion and check the harmonicity of such submersions. We also foind necessary and sufficient conditions for a semi- invariant semi-Riemannian submersion to be totally geodesic. Moreover, we obtain curvature relations between the base manifold and the total manifold. [ABSTRACT FROM AUTHOR]

We introduce the concept of para-contact product semi-Riemannian submersions from an almost para-contact metric manifold onto a semi-Riemannian product manifold. We provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost para-contact structure of the total manifold. Moreover, we investigate various properties of the O'Neill's tensors of such submersions, find the integrability of the horizontal distribution. The paper is also focused on the transference of structures defined on the total manifold. [ABSTRACT FROM AUTHOR]

In this paper, we introduce slant submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic. [ABSTRACT FROM AUTHOR]