On twisted Riemannian extensions associated with Szab o metrics

Abstract

Let $M$ be an n-dimensional manifold with a torsion free a fine connection $\nabla$ and let $T^*M$ be the cotangent bundle. In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afi ne geometry of $(M,\nabla)$ and the neutral signature pseudo-Riemannian geometry of $T^*M$. We investigate the spectral geometry of the Szabo operator on $M$ and on $T^*M$.