Browse > Article
http://dx.doi.org/10.4134/CKMS.2012.27.4.771

BIMINIMAL CURVES IN 2-DIMENSIONAL SPACE FORMS  

Inoguchi, Jun-Ichi (Department of Mathematical Sciences Faculty of Science)
Lee, Ji-Eun (Institute of Mathematical Sciences Ewha Womans University)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.4, 2012 , pp. 771-780 More about this Journal
Abstract
We study biminimal curves in 2-dimensional Riemannian manifolds of constant curvature.
Keywords
biminimal curves; elliptic functions;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Inoguchi, Biharmonic curves in Minkowski 3-space, Int. J. Math. Math. Sci. 2003 (2003), no. 21, 1365-1368   DOI   ScienceOn
2 J. Inoguchi, Biharmonic curves in Minkowski 3-space, part II, Int. J. Math. Math. Sci. 2006 (2006), Article ID 92349, 4 pages.
3 J. Inoguchi, Submanifolds with harmonic mean curvature vector field in contact 3-manifolds, Colloq. Math. 100 (2004), no. 2, 163-179.   DOI
4 J. Inoguchi and J.-E. Lee, Almost contact curves in normal almost contact 3-manifolds, submitted.
5 J. Langer and D. A. Singer, The total squared curvature of closed curves, J. Differential Geom. 20 (1984), no. 1, 1-22.   DOI
6 E. Loubeau and S. Montaldo, Biminimal immersions, Proc. Edinb. Math. Soc. (2) 51 (2008), no. 2, 421-437.
7 S. Montaldo and C. Oniciuc, A short survey on biharmonic maps between Riemannian manifolds, Rev. Un. Mat. Argentina 47 (2006), no. 2, 1-22.
8 H. Urakawa, Calculus of Variation and Harmonic Maps, Transl. Math. Monograph. 132, Amer. Math. Soc., Providence, 1993.
9 R. Caddeo, S. Montaldo, and P. Piu, Biharmonic curves on a surface, Rend. Mat. Appl. (7) 21 (2001), no. 1-4, 143-157.
10 B. Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337.
11 B. Y. Chen and S. Ishikawa, Biharmonic surfaces in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ. Ser. A 45 (1991), no. 2, 323-347.
12 J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMS Regional Conference Series in Mathematics, 50., American Mathematical Society, Providence, RI, 1983.
13 J. Eells and J. H. Sampson, Variational theory in fibre bundles, Proc. U.S.-Japan Seminar in Differential Geometry, pp. 22-3 Nippon Hyoronsha, Tokyo, 1966.