Principal torus bundles of Lorentzian ${\mathcal S}$-manifolds and the φ-null Osserman condition

Abstract

In this short note we provide a few results about the projectability of the φ-null Osserman condition onto the classical and the null-Osserman condition, via semi-Riemannian submersions as projection maps of principal torus bundles induced by a Lorentzian ${\mathcal S}$-manifold.