A new obstruction to minimal isometric immersions into a real space form

In the theory of minimal submanifold, the following problem is fundamental: when does a given Riemannian manifold admit (or does not admit) a minimal isometric immersion into an Euclidean space form of arbitrary dimension? A partial solution of this problem was obtained by B.Y. Chen as an application of his fundamental inequality [1]. In this paper we obtain another partial solution of this problem.