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On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator

Yıl 2017, Cilt: 10 Sayı: 1, 96 - 111, 30.04.2017
https://doi.org/10.36890/iejg.584449

Öz

Kaynakça

  • [1] Arvanitoyeorgos, A., Defever, F. and Kaimakamis, G., Hypersurfaces of E4 with proper mean curvature vector. J. Math. Soc. Japan, 59 (2007), 3, 797-809.
  • [2] Arvanitoyeorgos, A., Defever, F., Kaimakamis, G. and Papantoniou, V., Biharmonic Lorentzian hypersurfaces in E4. Pac. J. Math. 229(2007), 2, 293-305.
  • [3] Chen, B. Y., Total Mean Curvature and Submanifolds of Finite Type. World Scientific, Singapore, 1984.
  • [4] Chen, B. Y., Submanifolds of finite type and applications. Proc. Geometry and Topology Research Center, Taegu, 3 (1993), 1-48.
  • [5] Chen, B. Y., A report on submanifolds of finite type. Soochow J. Math., 22 (1996); 22: 117-337.
  • [6] Chen, B. Y., Classification of marginally trapped Lorentzian flat surfaces in E4 and its application to biharmonic surfaces. J. Math. Anal. Appl., 340(2008), 861-875.
  • [7] Chen, B. Y. and Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces. Mem. Fac. Sci. Kyushu Univ. A., 45 (1991), 323-347.
  • [8] Chen, B. Y. and Ishikawa, S., Biharmonic pseudo-Riemannian submanifolds in pseudo-Euclidean spaces. Kyushu J. Math., 52 (1998), 1-18.
  • [9] Dimitric, I., Quadratic representation and submanifolds of finite type. Doctoral thesis, Michigan State University, 1989.
  • [10] Deepika and Gupta, R. S., Biharmonic hypersurfaces in E5 with zero scalar curvature. Afr. Diaspora J. Math., 18 (2015), 1, 12-26.
  • [11] Fu, Y., Biharmonic hypersurfaces with three distinct principal curvatures in the Euclidean 5-space, Journal of Geometry and Physics, 75(2014), 113-119.
  • [12] Gupta, R. S., On biharmonic hypersurfaces in Euclidean space of arbitrary dimension. Glasgow Math. J., 57 (2015), 633-642.
  • [13] Gupta, R. S., Biharmonic hypersurfaces in E5. An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.),Tomul LXII (2016), f. 2, vol. 2, 585-593.
  • [14] Hasanis, Th. and Vlachos, Th., Hypersurfaces in E4 with harmonic mean curvature vector field. Math. Nachr., 172 (1995), 145-169.
  • [15] Magid, M. A., Lorentzian isoparametric hypersurfaces. Pacific J. Math., 118(1985), 165-197.. Z., Einstein spaces. Pergamon Press, Oxford, 1969.
Yıl 2017, Cilt: 10 Sayı: 1, 96 - 111, 30.04.2017
https://doi.org/10.36890/iejg.584449

Öz

Kaynakça

  • [1] Arvanitoyeorgos, A., Defever, F. and Kaimakamis, G., Hypersurfaces of E4 with proper mean curvature vector. J. Math. Soc. Japan, 59 (2007), 3, 797-809.
  • [2] Arvanitoyeorgos, A., Defever, F., Kaimakamis, G. and Papantoniou, V., Biharmonic Lorentzian hypersurfaces in E4. Pac. J. Math. 229(2007), 2, 293-305.
  • [3] Chen, B. Y., Total Mean Curvature and Submanifolds of Finite Type. World Scientific, Singapore, 1984.
  • [4] Chen, B. Y., Submanifolds of finite type and applications. Proc. Geometry and Topology Research Center, Taegu, 3 (1993), 1-48.
  • [5] Chen, B. Y., A report on submanifolds of finite type. Soochow J. Math., 22 (1996); 22: 117-337.
  • [6] Chen, B. Y., Classification of marginally trapped Lorentzian flat surfaces in E4 and its application to biharmonic surfaces. J. Math. Anal. Appl., 340(2008), 861-875.
  • [7] Chen, B. Y. and Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces. Mem. Fac. Sci. Kyushu Univ. A., 45 (1991), 323-347.
  • [8] Chen, B. Y. and Ishikawa, S., Biharmonic pseudo-Riemannian submanifolds in pseudo-Euclidean spaces. Kyushu J. Math., 52 (1998), 1-18.
  • [9] Dimitric, I., Quadratic representation and submanifolds of finite type. Doctoral thesis, Michigan State University, 1989.
  • [10] Deepika and Gupta, R. S., Biharmonic hypersurfaces in E5 with zero scalar curvature. Afr. Diaspora J. Math., 18 (2015), 1, 12-26.
  • [11] Fu, Y., Biharmonic hypersurfaces with three distinct principal curvatures in the Euclidean 5-space, Journal of Geometry and Physics, 75(2014), 113-119.
  • [12] Gupta, R. S., On biharmonic hypersurfaces in Euclidean space of arbitrary dimension. Glasgow Math. J., 57 (2015), 633-642.
  • [13] Gupta, R. S., Biharmonic hypersurfaces in E5. An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.),Tomul LXII (2016), f. 2, vol. 2, 585-593.
  • [14] Hasanis, Th. and Vlachos, Th., Hypersurfaces in E4 with harmonic mean curvature vector field. Math. Nachr., 172 (1995), 145-169.
  • [15] Magid, M. A., Lorentzian isoparametric hypersurfaces. Pacific J. Math., 118(1985), 165-197.. Z., Einstein spaces. Pergamon Press, Oxford, 1969.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Deepika Gupta Bu kişi benim

Ram Shankar Gupta Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 10 Sayı: 1

Kaynak Göster

APA Gupta, D., & Gupta, R. S. (2017). On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator. International Electronic Journal of Geometry, 10(1), 96-111. https://doi.org/10.36890/iejg.584449
AMA Gupta D, Gupta RS. On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator. Int. Electron. J. Geom. Nisan 2017;10(1):96-111. doi:10.36890/iejg.584449
Chicago Gupta, Deepika, ve Ram Shankar Gupta. “On Biharmonic Lorentz Hypersurfaces With Non-Diagonal Shape Operator”. International Electronic Journal of Geometry 10, sy. 1 (Nisan 2017): 96-111. https://doi.org/10.36890/iejg.584449.
EndNote Gupta D, Gupta RS (01 Nisan 2017) On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator. International Electronic Journal of Geometry 10 1 96–111.
IEEE D. Gupta ve R. S. Gupta, “On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator”, Int. Electron. J. Geom., c. 10, sy. 1, ss. 96–111, 2017, doi: 10.36890/iejg.584449.
ISNAD Gupta, Deepika - Gupta, Ram Shankar. “On Biharmonic Lorentz Hypersurfaces With Non-Diagonal Shape Operator”. International Electronic Journal of Geometry 10/1 (Nisan 2017), 96-111. https://doi.org/10.36890/iejg.584449.
JAMA Gupta D, Gupta RS. On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator. Int. Electron. J. Geom. 2017;10:96–111.
MLA Gupta, Deepika ve Ram Shankar Gupta. “On Biharmonic Lorentz Hypersurfaces With Non-Diagonal Shape Operator”. International Electronic Journal of Geometry, c. 10, sy. 1, 2017, ss. 96-111, doi:10.36890/iejg.584449.
Vancouver Gupta D, Gupta RS. On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator. Int. Electron. J. Geom. 2017;10(1):96-111.