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

TL;DR

This paper explores the relationships between various Osserman conditions on Lorentzian S-manifolds, using semi-Riemannian submersions of principal torus bundles to establish connections among them.

Contribution

It establishes new links between {}-null, null, and classical Osserman conditions via semi-Riemannian submersions in Lorentzian S-manifolds.

Findings

Connections between Osserman conditions established

Semi-Riemannian submersions relate different Osserman conditions

Principal torus bundles serve as a framework for these relationships

Abstract

The main result we give in this brief note relates, under suitable hypotheses, the {\phi}-null Osserman, the null Osserman and the classical Osserman conditions to each other, via semi-Riemannian submersions as projection maps of principal torus bundles arising from a Lorentzian S-manifold.