References
- K. Akutagawa and S. Maeta, Biharmonic properly immersed submanifolds in Euclidean spaces, Geom. Dedicata 164 (2013), 351-355. https://doi.org/10.1007/s10711-012-9778-1
- Y. Alexieva, G. Ganchev, and V. Milousheva, On the theory of Lorentz surfaces with parallel normalized mean curvature vector field in pseudo-Euclidean 4-space, J. Korean Math. Soc. 53 (2016), no. 5, 1077-1100. https://doi.org/10.4134/JKMS.j150381
- L. J. Alias and N. Ertug Gurbuz, An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures, Geom. Dedicata 121 (2006), 113-127. https://doi.org/10.1007/s10711-006-9093-9
- A. Arvanitoyeorgos, F. Defever, and G. Kaimakamis, Hypersurfaces of E4s with proper mean curvature vector, J. Math. Soc. Japan 59 (2007), no. 3, 797-809. http://projecteuclid.org/euclid.jmsj/1191591858
- A. Arvanitoyeorgos, F. Defever, G. Kaimakamis, and V. J. Papantoniou, Biharmonic Lorentz hypersurfaces in E41, Pacific J. Math. 229 (2007), no. 2, 293-305. https://doi.org/10.2140/pjm.2007.229.293
- B.-Y. Chen, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), no. 2, 169-188.
-
F. Defever, Hypersurfaces of
${\bar{E}}^4$ satisfying${\Delta}{\vec{H}}={\lambda}{\vec{H}}$ , Michigan Math. J. 44 (1997), no. 2, 355-363. https://doi.org/10.1307/mmj/1029005710 - I. M. Dimitric, Submanifolds of Em with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica 20 (1992), no. 1, 53-65.
- T. Hasanis and T. Vlachos, Hypersurfaces in E4 with harmonic mean curvature vector field, Math. Nachr. 172 (1995), no. 1, 145-169. https://doi.org/10.1002/mana.19951720112
- S. M. B. Kashani, On some L1-finite type (hyper)surfaces in ℝn+1, Bull. Korean Math. Soc. 46 (2009), no. 1, 35-43. https://doi.org/10.4134/BKMS.2009.46.1.035
- P. Lucas and H. F. Ramirez-Ospina, Hypersurfaces in the Lorentz-Minkowski space satisfying Lkψ = Aψ + b, Geom. Dedicata 153 (2011), 151-175. https://doi.org/10.1007/s10711-010-9562-z
- M. A. Magid, Lorentzian isoparametric hypersurfaces, Pacific J. Math. 118 (1985), no. 1, 165-197. http://projecteuclid.org/euclid.pjm/1102706671 102706671
- B. O'Neill, Semi-Riemannian Geometry, Pure and Applied Mathematics, 103, Academic Press, Inc., New York, 1983.
- F. Pashaie, An extension of biconservative timelike hypersurfaces in Einstein space, Proyecciones 41 (2022), no. 1, 335-351.
- F. Pashaie and S. M. B. Kashani, Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying Lkx = Ax+b, Bull. Iranian Math. Soc. 39 (2013), no. 1, 195-213.
- F. Pashaie and S. M. B. Kashani, Timelike hypersurfaces in the standard Lorentzian space forms satisfying Lkx = Ax + b, Mediterr. J. Math. 11 (2014), no. 2, 755-773. https://doi.org/10.1007/s00009-013-0336-3
- F. Pashaie, A. Mohammadpouri, Lk-biharmonic spacelike hypersurfaces in Minkowski 4-space 𝔼41, Sahand Comm. Math. Anal., 5:1 (2017), 21-30.
- A. Petrov, Einstein Spaces, translated from the Russian by R. F. Kelleher, translation edited by J. Woodrow, Pergamon, Oxford, 1969.
- R. C. Reilly, Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Differential Geom. 8 (1973), no. 3, 465-477. https://doi.org/10.4310/jdg/1214431802
- F. Torralbo and F. Urbano, Surfaces with parallel mean curvature vector in 𝕊2 × 𝕊2 and ℍ2 × ℍ2, Trans. Amer. Math. Soc. 364 (2012), no. 2, 785-813. https://doi.org/10.1090/S0002-9947-2011-05346-8
- G. Wei, Complete hypersurfaces in a Euclidean space ℝn+1 with constant mth mean curvature, Differential Geom. Appl. 26 (2008), no. 3, 298-306. https://doi.org/10.1016/j.difgeo.2007.11.021