A non-existence theorem for isometric immersions

Let f : M -> (M) over bar be an isometric immersion between Riemannian manifolds. For certain conditions on M and (M) over bar in terms Of Curvatures and external diameter, we extend the non-embedding theorem of Chern and Kuiper to the isometric immersions of non-compact manifolds. Also, Our results generalize and improve the main results of Jorge and Koutroufiotis [L. Jorge. D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (4) (1981) 711-725] and Veeravalli [A. R. Veeravalli, A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms, Bull. Austral. Math. Soc. 62 (1) (2000) 165-170]. (C) 2008 Elsevier B.V. All rights reserved.