Abstract: In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically im- mersed hypersurface x : Mn ! En+1 is said to be biharmonic if 2x = 0, where is the Laplace operator. We study the Lr-biharmonic hypersur- faces as a generalization of biharmonic ones, where Lr is the linearized operator of the (r + 1)th mean curvature of the hypersurface and in spe- cial case we have L0 = . We prove that Lr-biharmonic hypersurface of Lr- nite type and also Lr-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.
