Absolute continuity of the periodic Schrödinger operator in transversal geometry

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We show that the spectrum of a Schrödinger operator on Rⁿ, n≥ 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 Lⁿ/²loc(Rⁿ), 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.