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

Yıl 2014, Cilt: 7 Sayı: 2, 1 - 6, 30.10.2014
https://doi.org/10.36890/iejg.593970

Öz

 

Kaynakça

  • [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.
Yıl 2014, Cilt: 7 Sayı: 2, 1 - 6, 30.10.2014
https://doi.org/10.36890/iejg.593970

Öz

Kaynakça

  • [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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Bogdan D. Suceavă

Yayımlanma Tarihi 30 Ekim 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 7 Sayı: 2

Kaynak Göster

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. Ekim 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, sy. 2 (Ekim 2014): 1-6. https://doi.org/10.36890/iejg.593970.
EndNote Suceavă BD (01 Ekim 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., c. 7, sy. 2, ss. 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 (Ekim 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, c. 7, sy. 2, 2014, ss. 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.