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http://dx.doi.org/10.4134/JKMS.2008.45.2.393

BIHARMONIC LEGENDRE CURVES IN SASAKIAN SPACE FORMS  

Fetcu, Dorel (DEPARTMENT OF MATHEMATICS "GH. ASACHI" TECHNICAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 393-404 More about this Journal
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;
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1 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
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   DOI
3 N. Ekmekci and N. Yaz, Biharmonic general helices in contact and Sasakian manifolds, Tensor (N.S.) 65 (2004), no. 2, 103-108
4 D. Fetcu, Biharmonic curves in the generalized Heisenberg group, Beitrage Algebra Geom. 46 (2005), no. 2, 513-521   DOI   ScienceOn
5 J. Inoguchi, Submanifolds with harmonic mean curvature vector field in contact 3-manifolds, Colloq. Math. 100 (2004), no. 2, 163-179   DOI
6 C. Baikoussis and D. E. Blair, On the geometry of the 7-sphere, Results Math. 27 (1995), no. 1-2, 5-16   DOI
7 S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-717
8 S. Tanno, Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations, Tohoku Math. J. (2) 23 (1971), 313-333   DOI
9 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
10 D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, MA, 2002
11 R. Caddeo, S. Montaldo, and C. Oniciuc, Biharmonic submanifolds in spheres, Israel J. Math. 130 (2002), 109-123   DOI
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 J. T. Cho, J. Inoguchi, and J. E. Lee, Biharmonic curves in 3-dimensional Sasakian space forms, Ann. Math. Pura Appl., to appear
14 G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7 (1986), no. 4, 389-402
15 Y.-Y. Kuo, On almost contact 3-structure, Tohoku Math. J. (2) 22 (1970), 325-332   DOI
16 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
17 T. Sasahara, Legendre surfaces whose mean curvature vectors are eigenvectors of the Laplace operator, Note Mat. 22 (2003/04), no. 1, 49-58
18 T. Sasahara, Legendre surfaces in Sasakian space forms whose mean curvature vectors are eigenvectors, Publ. Math. Debrecen 67 (2005), no. 3-4, 285-303