BIHARMONIC LEGENDRE CURVES IN SASAKIAN SPACE FORMS

Title & Authors
BIHARMONIC LEGENDRE CURVES IN SASAKIAN SPACE FORMS
Fetcu, Dorel;

Abstract
Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.
Keywords
Sasakian space form;Legendre curve;biharmonic curve;
Language
English
Cited by
1.
BIHARMONIC CURVES IN FINSLER SPACES,;

대한수학회지, 2014. vol.51. 6, pp.1105-1122
1.
Affine biharmonic submanifolds in 3-dimensional pseudo-Hermitian geometry, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2009, 79, 1, 113
2.
On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collectanea Mathematica, 2014, 65, 2, 203
3.
BIHARMONIC CURVES INTO QUADRICS, Glasgow Mathematical Journal, 2015, 57, 01, 131
4.
Slant curves in three-dimensional f-Kenmotsu manifolds, Journal of Mathematical Analysis and Applications, 2012, 394, 1, 400
5.
Unitary vector fields are Fermi–Walker transported along Rytov–Legendre curves, International Journal of Geometric Methods in Modern Physics, 2015, 12, 10, 1550111
6.
SLANT CURVES AND PARTICLES IN THREE-DIMENSIONAL WARPED PRODUCTS AND THEIR LANCRET INVARIANTS, Bulletin of the Australian Mathematical Society, 2013, 88, 01, 128
7.
Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry, Czechoslovak Mathematical Journal, 2014, 64, 4, 945
8.
BIHARMONIC CURVES IN FINSLER SPACES, Journal of the Korean Mathematical Society, 2014, 51, 6, 1105
9.
Explicit formulas for biharmonic submanifolds in Sasakian space forms, Pacific Journal of Mathematics, 2009, 240, 1, 85
10.
Slant Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds, Mediterranean Journal of Mathematics, 2014, 11, 3, 965
11.
Slant Curves in 3-dimensional Normal Almost Contact Geometry, Mediterranean Journal of Mathematics, 2013, 10, 2, 1067
References
1.
C. Baikoussis and D. E. Blair, On the geometry of the 7-sphere, Results Math. 27 (1995), no. 1-2, 5-16

2.
C. Baikoussis, D. E. Blair, and T. Koufogiorgos, Integral submanifolds of Sasakian space forms $\bar{M}^7$, Results Math. 27 (1995), no. 3-4, 207-226

3.
D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, MA, 2002

4.
R. Caddeo, S. Montaldo, and C. Oniciuc, Biharmonic submanifolds in spheres, Israel J. Math. 130 (2002), 109-123

5.
J. T. Cho, J. Inoguchi, and J. E. Lee, Biharmonic curves in 3-dimensional Sasakian space forms, Ann. Math. Pura Appl., to appear

6.
J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMS Regional Conference Series in Mathematics, 50. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1983

7.
N. Ekmekci and N. Yaz, Biharmonic general helices in contact and Sasakian manifolds, Tensor (N.S.) 65 (2004), no. 2, 103-108

8.
D. Fetcu, Biharmonic curves in the generalized Heisenberg group, Beitrage Algebra Geom. 46 (2005), no. 2, 513-521

9.
J. Inoguchi, Submanifolds with harmonic mean curvature vector field in contact 3-manifolds, Colloq. Math. 100 (2004), no. 2, 163-179

10.
G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7 (1986), no. 4, 389-402

11.
Y.-Y. Kuo, On almost contact 3-structure, Tohoku Math. J. (2) 22 (1970), 325-332

12.
S. Montaldo and C. Oniciuc, A short survey on biharmonic maps between riemannian manifolds, Rev. Un. Mat. Argentina 47 (2006), no. 2, 1-22

13.
V. Oproiu and N. Papaghiuc, Some results on harmonic sections of cotangent bundles, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 45 (1999), no. 2, 275-290

14.
T. Sasahara, Legendre surfaces whose mean curvature vectors are eigenvectors of the Laplace operator, Note Mat. 22 (2003/04), no. 1, 49-58

15.
T. Sasahara, Legendre surfaces in Sasakian space forms whose mean curvature vectors are eigenvectors, Publ. Math. Debrecen 67 (2005), no. 3-4, 285-303

16.
S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-717

17.
S. Tanno, Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations, Tohoku Math. J. (2) 23 (1971), 313-333

18.
H. Urakawa, Calculus of Variations and Harmonic Maps, Translated from the 1990 Japanese original by the author. Translations of Mathematical Monographs, 132. American Mathematical Society, Providence, RI, 1993