[1] K. Akutagawa and S. Maeta. Biharmonic properly immersed submanifolds in Euclidean spaces. Geom.
Ded., 164:351–355, 2013.
[2] L. J. Al´ıas, S. C. Garc´ıa-Mart´ınez, and M. Rigoli. Biharmonic hypersurfaces in complete Riemannian
manifolds. Pacific. J. Math, 263:1–12, 2013.
[3] L. J. Al´ıas and N. G¨urb¨uz. An extension of Takahashi theorem for the linearized operators of the
higher order mean curvatures. Geom. Ded., 121:113–127, 2006.
[4] L. J. Al´ıas and S. M. B. Kashani. Hypersurfaces in space forms satisfying the condition lkx = ax+b.
Taiwanese J.M., 14:1957–1977, 2010.
[5] M. Aminian. Introduction of T-harmonic maps. to appear in Pure Appl. Math.
[6] M. Aminian. Lk-biharmonic hypersurfaces in space forms with three distinct principal curvatures.
Commun. Korean Math. Soc., 35(4):1221–1244, 2020.
[7] M. Aminian and S. M. B. Kashani. Lk-biharmonic hypersurfaces in the Euclidean space. Taiwanese
J.M., 19:861–874, 2015.
[8] M. Aminian and S. M. B. Kashani. Lk-biharmonic hypersurfaces in space forms. Acta Math. Vietnam.,
42:471–490, 2017.
[9] M. Aminian and M. Namjoo. fLk-harmonic maps and fLk-harmonic morphisms. Acta Math. Vietnam.,
2020.
[10] A. Balmus¸, S. Montaldo, and C. Oniciuc. Classification results and new examples of proper biharmonic
submanifolds in spheres. Note Mat., suppl. n. 1:49–61, 2008.
[11] A. Balmus¸, S. Montaldo, and C. Oniciuc. New results toward the classification of biharmonic submanifolds
in Sn. An. S¸t. Univ. Ovidius Constant¸a, 20:89–114, 2012.
[12] J. L. M. Barbosa and A. G. Colares. Stability of hypersurfaces with constant r-mean curvature. Ann.
GlobalAnal. Geom., 15:277–297, 1997.
[13] R. Caddeo, S. Montaldo, and C. Oniciuc. Biharmonic submanifolds of S3. Inter. J. Math., 12:867–876,
2001.
[14] B. Y. Chen. Some open problems and conjectures on submanifolds of finite type. Soochow J. Math.,
17:169–188, 1991.
[15] B. Y. Chen. Total Mean Curvature and Submanifold of Finite Type. Series in Pure Math. World Scientific,
2nd edition, 2014.
[16] B. Y. Chen and M. I. Munteanu. Biharmonic ideal hypersurfaces in Euclidean spaces. Diff. Geom.
Appl., 31:1–16, 2013.
[17] S. Y. Cheng and S. T. Yau. Hypersurfaces with constant scalar curvature. Math. Ann., 225:195–204,
1977.
[18] F. Defever. Hypersurfaces of E4 with harmonic mean curvature vector. Math. Nachr., 196:61–69,
1998.
[19] I. Dimitri´c. Submanifolds of Em with harmonic mean curvature vector. Bull. Inst. Math. Acad. Sinica,
20:53–65, 1992.
[20] J. Eells and J. H. Sampson. Harmonic mappings of Riemannian manifolds. Amer. J. Math., 86:109–
160, 1964.
[21] T. Hasanis and T. Vlachos. Hypersurfaces in E4 with harmonic mean curvature vector field. Math.
Nachr., 172:145–169, 1995.
[22] G. Y. Jiang. 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math.,
7A:388–402, 1986. the English translation, Note di Mathematica, 28 (2008) 209-232.
[23] N. Nakauchi and H. Urakawa. Biharmonic submanifolds in a Riemannian manifold with nonpositive
curvature. Results. Math., 63:467–471, 2013.
[24] Y. L. Ou. Biharmonic hypersurfaces in Riemannian manifolds. Pacific J. Math., 248:217–232, 2010.
[25] Y. L. Ou and L. Tang. On the generalized chen’s conjecture on biharmonic submanifolds. Michigan
Math. J., 61:531–542, 2012.
[26] R. C. Reilly. Variational properties of functions of the mean curvatures for hypersurfaces in space
forms. J. Diff. Geom., 8:465–477, 1973.
[27] H. Rosenberg. Hypersurfaces of constant curvature in space forms. Bull. Sci. Math., 117:211–239,
1993.