Semi-invariant semi-Riemannian submersions

Abstract

Abstract. 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 de…nition of a semi-Riemannian submersion and check the harmonicity of such submersions. We also …nd necessary and su¢ cient conditions for a semiinvariant semi-Riemannian submersion to be totally geodesic. Moreover, we obtain curvature relations between the base manifold and the total manifold.