Lk-BIHARMONIC HYPERSURFACES IN THE EUCLIDEAN SPACE
نویسندگان
چکیده
Chen conjecture states that every Euclidean biharmonic submanifold is minimal. In this paper we consider the Chen conjecture for Lk-operators. The new conjecture (Lk-conjecture) is formulated as follows: If Lkx = 0 then Hk+1 = 0 where x : M → R is an isometric immersion of a Riemannian manifold M into the Euclidean space R, Hk+1 is the (k+1)-th mean curvature of M , and Lk is the linearized operator of the (k + 1)-th mean curvature of the Euclidean hypersurface M . We prove the Lk-conjecture for the hypersurface M with at most two principal curvatures.
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