Biharmonic hypersurfaces in a Riemannian manifold with non-positive Ricci curvature

In this article, we show that, for a biharmonic hypersurface (M, g) of a Riemannian manifold (N, h) of non-positive Ricci curvature, if ò_M|H|² v_g < ￥{\int_M\vert H\vert^2 v_g<\infty}, where H is the mean curvature of (M, g) in (N, h), then (M, g) is minimal in (N, h). Thus, for a counter example (M, g) in the case of hypersurfaces to the generalized Chen’s conjecture (cf. Sect. 1), it holds that ò_M|H|² v_g=￥{\int_M\vert H\vert^2 v_g=\infty} .