TY - JOUR T1 - AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4 AU - Suceavă, Bogdan D. PY - 2014 DA - October DO - 10.36890/iejg.593970 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 1 EP - 6 VL - 7 IS - 2 LA - en AB -   KW - principal curvatures KW - scalar curvature KW - shape operator KW - umbilical hypersurfaces KW - mean curvature KW - Gauss-Kronecker curvature CR - [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. CR - [2] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math., 60 (1993), 568–578. CR - [3] Chen, B.-Y., Mean curvature and shape operator of isometric immersions in real-space- forms, Glasgow Math.J. 38 (1996), 87–97. CR - [4] Chen, B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J., 41 (1999), 33–41. CR - [5] Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japanese J. Math., 26 (2000), 105–127. CR - [6] Chen, B.-Y., Pseudo-Riemannian geometry, δ-invariants and applications, World Scien- tific, 2011. CR - [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. CR - [8] Cvetkovski, Z., Inequalities. Theorems, Techniques and Selected Problems, Springer- Verlag, 2012. CR - [9] do Carmo, M. P., Riemannian Geometry, Birkhäuser, 1992. CR - [10] Hardy, G. H., Littlewood, J. E. and P´olya, G., Inequalities (Cambridge Mathematical Library), Cambridge University Press; 2 edition, 1988. CR - [11] Hasanis, Th. and Vlachos, Th., Hypersurfaces in E4 with harmonic mean curvature vector field, Math. Nachr. 172 (1995), 145–169. CR - [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. CR - [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. CR - [14] Suceava˘, B. D., The amalgamatic curvature and the orthocurvatures of three dimen- sional hypersurfaces in E4 (to appear). CR - [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. UR - https://doi.org/10.36890/iejg.593970 L1 - https://dergipark.org.tr/en/download/article-file/765219 ER -