The Mixed Scalar Curvature of a Twisted Product Riemannian Manifolds and Projective Submersions

Abstract

In the present paper, we study twisted and warped products of Riemannian manifolds. As an application, we consider projective submersions of Riemannian manifolds, since any Riemannian manifold admitting a projective submersion is necessarily a twisted product of some two Riemannian manifolds.