[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
[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.
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.