Absolute continuity of the periodic Schrödinger operator in transversal geometry

Abstract

We show that the spectrum of a Schrödinger operator on ${\mathbb{R}}^n$, $n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric potential in $L_{\text{loc}}^{n/2}({\mathbb{R}}^n)$, is purely absolutely continuous. Previously known results in the case of a general metric are obtained in [12], see also [8], under the assumption that the metric, as well as the potential, are reflection symmetric.