آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,005 |
| تعداد دریافت فایل اصل مقاله | 3,580,078 |
Biharmonic hypersurfaces in the standard Lorentz 5-pseudosphere | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 2 - شماره پیاپی 32، مرداد 2025، صفحه 203-219 اصل مقاله (542.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24319.1716 | ||
| نویسندگان | ||
| Ghorbanali Haghighatdoos1؛ Sara Hoseinpour1؛ Firooz Pashaie* 2؛ Leila Shahbaz2 | ||
| 1Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran | ||
| 2Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, Maragheh, Iran | ||
| چکیده | ||
| In this manuscript, we study the Lorentz hypersurfaces of the Lorentz 5-pseudosphere (i.e. the pseudo-Euclidean 5-sphere) $S^5_1$ having three distinct principal curvatures. A well-known conjecture of Bang-Yen Chen on Euclidean spaces says that every submanifold is minimal. We consider an advanced version of the conjecture on Lorentz hypersurfaces of $S^5_1$. We present an affirmative answer to the extended conjecture on Lorentz hypersurfaces with three distinct principal curvatures. | ||
| کلیدواژه‌ها | ||
| C-biharmonic؛ isoparametric؛ de-Sitter space؛ 1-minimal | ||
| مراجع | ||
|
[1] Akutagawa, K., Maeta, S. (2013), Biharmonic properly immersed submanifolds in Euclidean spaces, Geom. Dedicata, 164, 351-355. http://doi:10.1007/s10711-012-9778-1.
[2] Alias, L.J., Gurbuz, N. (2006), An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures, Geom. Dedicata, 121, 113-127. http://doi:10.1007/s10711-006-9093-9.
[3] Arvanitoyeorgos, A., Defever, F., Kaimakamis, G., Papantoniou, B. J. (2007), Biharmonic Lorentz hypersurfaces in E4 1 , Paci c J. Math., 229, 293-306. http://doi:10.2140/pjm.2007.229.293 [4] Chen, B. Y. (2014), Some open problems and conjetures on submanifolds of nite type: Recent development, Tamkang J. Math., 56, 87-108. http://doi:10.5556/tkjm.45.2014.1564.
[5] Defever, F. (1998), Hypersurfaces of E4 with harmonic mean curvature vector, Math. Nachr., 196, 61-69. https://doi.org/10.1002/mana.19981960104.
[6] Dimitric, I. (1992) Submanifolds of En with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sin., 20, 53-65. https://www.researchgate.net/publication/266138884.
[7] Gupta, R. S. (2016), Biharmonic hypersurfaces in E5s , An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.), 112:2, 585-593. [8] Hasanis, T. and Vlachos, T. (1995) Hypersurfaces in E4 with harmonic mean curvature vector eld, Math. Nachr., 172, 145-169. doi:10.1002/mana.19951720112. [9] Jiang, G. Y. (1987), The conservation law for 2-harmonic maps between Riemannian manifolds, Acta Math. Sin., 30, 220{225.
[10] Kashani, S. M. B. (2009), On some L1- nite type (hyper)surfaces in Rn+1, Bull. Korean Math. Soc., 46:1, 35-43. http://doi:10.4134/BKMS.2009.46.1.035.
[11] Lucas, P. and Ramirez-Ospina, H. F. (2011), Hypersurfaces in the Lorentz-Minkowski space satisfying Lk = A + b, Geom. Dedicata, 153, 151-175. http://doi:10.1007/s10711-010-9562-z.
[12] Magid, M. A. (1985), Lorentzian isoparametric hypersurfaces, Paci c J. of Math., 118:1, 165-197. http://doi:10.2140/PJM.1985.118.165.
[13] Pashaie, F. and Mohammadpouri, A. (2017), Lk-biharmonic spacelike hypersurfaces in Minkowski 4-space E41 , Sahand Comm. Math. Anal., 5:1 , 21-30. http://doi:10.22130/scma.2017.20589. [14] O'Neill, B. (1983), Semi-Riemannian Geometry with Applicatins to Relativity, 2nd edition, Academic Press Inc..
[15] Pashaie, F. and Kashani, S. M. B. (2013), Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying Lkx = Ax + b, Bull. Iran. Math. Soc., 39:1, 195{213. http://bims.iranjournals.ir/article338.html.
[16] Pashaie, F. and Kashani, S. M. B. (2014), Timelike hypersurfaces in the Lorentzian standard space forms satisfying Lkx = Ax + b, Mediterr. J. Math., 11:2, 755-773. https://link.springer.com/article/10.1007/s00009-013-0336-3.
[17] Petrov, A. Z. (1969), Einstein Spaces, Oxford and New York: Pergamon Press, Hungary.
[18] Turgay, N. C. (2014), Some classi cations of biharmonic Lorentzian hypersurfaces in Minkowski 5-space E51 , Mediterr. J. Math., 13:1, 401-412. http://doi: 10.1007/s00009-014-0491-1. | ||
|
آمار تعداد مشاهده مقاله: 110 تعداد دریافت فایل اصل مقاله: 82 |
||