On twisted Riemannian extensions associated with Szabó metrics

Abstract

Let M be an n-dimensional manifold with a torsion free affine connection ∇ 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 affine geometry of (M,∇) and the neutral signature pseudo-Riemannian geometry of T*M. We investigate the spectral geometry of the Szabó operator on M and on T*M.