SEMI-INVARIANT SEMI-RIEMANNIAN SUBMERSIONS

In this paper, we introduce semi-invariant semi-Riemannian sub-mersions from para-Kahler 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 find 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.