TY - JOUR T1 - L_1-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures TT - JF - IJMSI JO - IJMSI VL - 13 IS - 2 UR - http://ijmsi.ir/article-1-816-en.html Y1 - 2018 SP - 59 EP - 70 KW - Linearized operators L_r KW - L_1-biharmonic hypersurfaces KW - 1-minimal N2 - Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing Delta by its extension, L_1-operator (L_1-conjecture). The L_1-conjecture states that any L_1-biharmonic Euclidean hypersurface is 1-minimal. We prove that the L_1-conjecture is true for L_1-biharmonic hypersurfaces with three distinct principal curvatures and constant mean curvature of a Euclidean space of arbitrary dimension. M3 ER -