In this paper, we study f−biharmonic curves as the critical points of the f−bienergy functional. We give necessary and sufficient conditions for a curve having a timelike binormal vector lying on a 4-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an f−biharmonic curve. Moreover, we introduce proper f−biharmonic curves on the Lorentzian sphere S14.

1.
G.Y.
Jiang
,
2-harmonic isometric immersions between Riemannian manifolds
,
Chinese Ann. Math. Ser. A.
7
(
1986
),
130
144
.
2.
I.
Mihai
,
R.
Rosca
,
On Lorentzian P-Sasakian manifold in Classical Analysis
,
World Sci. Publ. River Edge, NJ
, pp.
155
169
,
1991
.
3.
I.
Sato
,
On a structure similar to the almost contact structure
,
Tensor N.S.
30
(
1976
),
219
224
.
4.
J.
Eells
,
J.H.
Sampson
,
Harmonic mapping of the Riemannian manifold
,
American J. Math.
86
(
1964
),
109
160
.
5.
J.
Walrave
,
Curves and surfaces in Minkowski spaces
, Doctoral Thesis,
K. U.
Leuven
,
Fac. of Science
,
1995
.
6.
K.
Matsumoto
,
On Lorentzian paracontact manifolds
,
Bull. Yamagota Univ. Natur. Sci.
12
(
1989
),
151
156
.
7.
K.
Matsumoto
,
I.
Mihai
,
R.
Rosca
,
ξ−null geodesic gradient vector fields on a Lorentzian para-Sasakian manifold
,
J. Korean Math. Soc.
32
(
1995
),
17
31
.
8.
M.M.
Tripathi
,
U.C.
De
,
Lorentzian almost paracontact manifolds and their submanifolds
,
J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math.
8
(
2001
),
101
125
.
9.
M.
Tarafdar
,
A.
Bhattacharyya
,
On Lorentzian para-Sasakian manifolds, in Steps in Differential Geometry (Debrecen)
.
Inst. Math. Infor.
(
2000
),
343
348
.
10.
M.C.
Chaki
,
B.
Gupta
,
On conformally symmetric spaces
,
Indian J. Math.
5
(
1963
),
113
122
.
11.
R.
Caddeo
,
S.
Montaldo
,
C.
Oniciuc
,
Biharmonic submanifolds of S3
,
Int. J. Math.
12
(
2001
),
867
876
.
12.
S.
Keleş
,
S.
Yüksel Perktaş
,
E.
Kılıç
,
Biharmonic Curves in LP-Sasakian Manifolds
,
Bull. Malays. Math. Sci. Soc.
33
(
2010
),
325
344
.
13.
S.
Montaldo
,
C.
Oniciuc
,
A short survey on biharmonic maps between Riemannian manifolds
,
Rev. Un. Mat. Argentina.
47
(
2006
),
1
22
.
14.
S.
Yü ksel Perktaş
,
E.
Kılıç
,
Biharmonic Maps between Doubly Warped Product Manifolds
,
Balkan Journal of Geometry and Its Applications.
15
(
2010
),
159
170
.
15.
S.
Yü ksel Perktaş
,
E.
Kılıç
,
S.
Keleş
, Biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds,
An. Stiint. Univ. Al. I
.
Cuza Iasi, Tomul LVII, f.2
DOI: ,
2011
.
16.
S.
Yü ksel Perktaş
,
E.
Kılıç
,
S.
Keleş
,
Hypersurfaces of Lorentzian para-Sasakian manifolds
,
Math. Scand.
108
(
2011
),
5
21
.
17.
W.-J.
Lu
,
On f −Biharmonic maps between Riemannian manifolds
, arXiv:1305.5478, preprint,
2013
.
18.
Y. -L.
Ou
,
Biharmonic hypersurfaces in Riemannian manifolds
,
Pacific J. of Math.
248
(
2010
),
217
232
.
19.
Y. -L.
Ou
,
On f −biharmonic maps and f −biharmonic submanifolds
,
Pacific J. of Math.
271
(
2014
),
461
477
.
This content is only available via PDF.
You do not currently have access to this content.