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On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator

Year 2017, Volume: 10 Issue: 1, 96 - 111, 30.04.2017
https://doi.org/10.36890/iejg.584449

Abstract

References

  • [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.
Year 2017, Volume: 10 Issue: 1, 96 - 111, 30.04.2017
https://doi.org/10.36890/iejg.584449

Abstract

References

  • [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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Deepika Gupta This is me

Ram Shankar Gupta This is me

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

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. April 2017;10(1):96-111. doi:10.36890/iejg.584449
Chicago Gupta, Deepika, and Ram Shankar Gupta. “On Biharmonic Lorentz Hypersurfaces With Non-Diagonal Shape Operator”. International Electronic Journal of Geometry 10, no. 1 (April 2017): 96-111. https://doi.org/10.36890/iejg.584449.
EndNote Gupta D, Gupta RS (April 1, 2017) On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator. International Electronic Journal of Geometry 10 1 96–111.
IEEE D. Gupta and R. S. Gupta, “On Biharmonic Lorentz Hypersurfaces with Non-Diagonal Shape Operator”, Int. Electron. J. Geom., vol. 10, no. 1, pp. 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 (April 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 and Ram Shankar Gupta. “On Biharmonic Lorentz Hypersurfaces With Non-Diagonal Shape Operator”. International Electronic Journal of Geometry, vol. 10, no. 1, 2017, pp. 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.