In this paper we study biharmonic hypersurfaces of semi-Euclidean spaces. We consider the Chen conjecture which states that the only biharmonic submanifolds of Euclidean spaces are the minimal ones. In particular, we obtain some conditions for biharmonic hypersurfaces in semi-Euclidean spaces. Finally, we give some examples for different conditions.

1.
B. Y.
Chen
and
S.
Ishikawa
,
Mem. Fac. Sci. Kyushu Univ. Ser. A
45
,
323
347
(
1991
).
2.
B. Y.
Chen
and
S.
Ishikawa
,
Kyushu J. Math.
52
,
167
185
(
1998
).
3.
B. Y.
Chen
and
M.
Munteanu
,
Differential Geometry and its Applications
31
,
1
16
(
2013
).
4.
B.
Kılıç
,
Commun. Fac. Sci. Univ. Ank. Series A1
54
,
13
20
(
2005
).
5.
B. Y.
Chen
,
Geometry of Submanifolds
(
M. Dekker
,
New York
,
1973
), pp.
44
45
.
6.
I.
Dimitric
,
Bull. Inst. Math. Acad. Sinica
20
,
56
57
(
1992
).
7.
K. L.
Duggal
and
B.
Şahin
,
Differential Geometry of Lightlike Submanifolds
(
Birkhauser Verlag A.G.
,
Berlin
,
2010
), pp.
37
409
.
This content is only available via PDF.
You do not currently have access to this content.