Vanishing theorems on hypersurfaces in Riemannian manifolds

We study a complete noncompact stable minimal hypersurface MM and a strongly stable hypersurface MM with constant mean curvature in a 5-dimensional Riemannian manifold NN. If NN is a compact simply connected manifold with bounded sectional curvature 517≤K̄≤1, then there is no nontrivial L2L2 harmonic form on MM. This is a generalized version of Tanno’s result on a stable minimal hypersurface in R5R5 and Zhu’s result on a stable minimal hypersurface in S5S5.