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AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4

Year 2014, Volume: 7 Issue: 2, 1 - 6, 30.10.2014
https://doi.org/10.36890/iejg.593970

Abstract

 

References

  • [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.
Year 2014, Volume: 7 Issue: 2, 1 - 6, 30.10.2014
https://doi.org/10.36890/iejg.593970

Abstract

References

  • [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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bogdan D. Suceavă

Publication Date October 30, 2014
Published in Issue Year 2014 Volume: 7 Issue: 2

Cite

APA Suceavă, B. D. (2014). AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4. International Electronic Journal of Geometry, 7(2), 1-6. https://doi.org/10.36890/iejg.593970
AMA Suceavă BD. AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4. Int. Electron. J. Geom. October 2014;7(2):1-6. doi:10.36890/iejg.593970
Chicago Suceavă, Bogdan D. “AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4”. International Electronic Journal of Geometry 7, no. 2 (October 2014): 1-6. https://doi.org/10.36890/iejg.593970.
EndNote Suceavă BD (October 1, 2014) AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4. International Electronic Journal of Geometry 7 2 1–6.
IEEE B. D. Suceavă, “AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4”, Int. Electron. J. Geom., vol. 7, no. 2, pp. 1–6, 2014, doi: 10.36890/iejg.593970.
ISNAD Suceavă, Bogdan D. “AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4”. International Electronic Journal of Geometry 7/2 (October 2014), 1-6. https://doi.org/10.36890/iejg.593970.
JAMA Suceavă BD. AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4. Int. Electron. J. Geom. 2014;7:1–6.
MLA Suceavă, Bogdan D. “AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4”. International Electronic Journal of Geometry, vol. 7, no. 2, 2014, pp. 1-6, doi:10.36890/iejg.593970.
Vancouver Suceavă BD. AN ESTIMATE FOR THE GAUSS-KRONECKER CURVATURE OF 3-DIMENSIONAL SMOOTH HYPERSURFACES IN E^4. Int. Electron. J. Geom. 2014;7(2):1-6.