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We add one more interesting family of Willmore tori to those already known [22, 12, 5, 6, 13]. The main result of this paper is a constructuon of the Willmore tori with umbilic lines. ... To construct these tori we use the methods of the integrable equations, These methods were already successfully applied [17, 24, 6, 7] to differential geometric classification of some submanifolds. In particular the case of constant mean curvature (CMC) surfaces in 3-dimensional space forms R^3, S^3, H^3 has received a airly complete treatment in [24, 5, 6].
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