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We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$,$n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiplehas a product structure with one Euclidean direction, and with a periodicelectric potential in $L^{n/2}_{\text{loc}}(\mathbb{R}^n)$, is purelyabsolutely continuous. Previously known results in the case of a general metricare obtained in [12], see also [8], under the assumption that the metric, aswell as the potential, are reflection symmetric.

Absolute continuity of the periodic Schr\"odinger operator in transversal geometry