___

• [1] Brzycki, B., Giesler, M., Gomez, K., Odom, L. H. and Suceavă, B. D., A Ladder of curvatures for hypersurfaces in Euclidean ambient space, to appear in Houston J. Math.
• [2] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math., 60 (1993), 568–578.
• [3] Chen, B.-Y., Mean curvature and shape operator of isometric immersions in real-space- forms, Glasgow Math.J. 38 (1996), 87–97.
• [4] Chen, B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J., 41 (1999), 33–41.
• [5] Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japanese J. Math., 26 (2000), 105–127.
• [6] Chen, B.-Y., Pseudo-Riemannian geometry, δ-invariants and applications, World Scien- tific, 2011.
• [7] Conley, C. T. R., Etnyre, R., Gardener, B., Odom, L. H. and Suceav˘a, B. D., New Curvature Inequalities for Hypersurfaces in the Euclidean Ambient Space, Taiwanese J. Math., 17 (3) (2013), 885–895.
• [8] Cvetkovski, Z., Inequalities. Theorems, Techniques and Selected Problems, Springer- Verlag, 2012.
• [9] do Carmo, M. P., Riemannian Geometry, Birkhäuser, 1992.
• [10] Hardy, G. H., Littlewood, J. E. and P´olya, G., Inequalities (Cambridge Mathematical Library), Cambridge University Press; 2 edition, 1988.
• [11] Hasanis, Th. and Vlachos, Th., Hypersurfaces in E4 with harmonic mean curvature vector field, Math. Nachr. 172 (1995), 145–169.
• [12] Hong, S., Matsumoto, K. and Tripathi, M., Certain basic inequalities for submanifolds of locally conformal Kaehler space forms, Sci. Univ. Tokyo Journal of Mathematics, Vol. 41, No. 1 (2005), 75-94.
• [13] Suceavă, B. D., Some remarks on B.-Y. Chen’s inequality involving classical invariants, Anal. Sti. Univ. ”Al.I.Cuza” Iasi, s.I.a, Math., 64 (1999), 405–412.
• [14] Suceava˘, B. D., The amalgamatic curvature and the orthocurvatures of three dimen- sional hypersurfaces in E4 (to appear).
• [15] Suceava˘, B. D. and Vajiac, M. B., Remarks on Chen’s fundamental inequality with classical curvature invariants in Riemannian Spaces, Annals Sti. Univ. “Al. I. Cuza”, s.I.a, Math. 54 (2008), no. 1, pp. 27–37.