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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)
  • Received : 2011.07.21
  • Published : 2012.10.31

Abstract

We study biminimal curves in 2-dimensional Riemannian manifolds of constant curvature.

Acknowledgement

Supported by : National Research Foundation of Korea

References

  1. R. Caddeo, S. Montaldo, and P. Piu, Biharmonic curves on a surface, Rend. Mat. Appl. (7) 21 (2001), no. 1-4, 143-157.
  2. B. Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337.
  3. 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.
  4. J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMS Regional Conference Series in Mathematics, 50., American Mathematical Society, Providence, RI, 1983.
  5. 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.
  6. J. Inoguchi, Biharmonic curves in Minkowski 3-space, Int. J. Math. Math. Sci. 2003 (2003), no. 21, 1365-1368 https://doi.org/10.1155/S016117120320805X
  7. J. Inoguchi, Biharmonic curves in Minkowski 3-space, part II, Int. J. Math. Math. Sci. 2006 (2006), Article ID 92349, 4 pages.
  8. J. Inoguchi, Submanifolds with harmonic mean curvature vector field in contact 3-manifolds, Colloq. Math. 100 (2004), no. 2, 163-179. https://doi.org/10.4064/cm100-2-2
  9. J. Inoguchi and J.-E. Lee, Almost contact curves in normal almost contact 3-manifolds, submitted.
  10. J. Langer and D. A. Singer, The total squared curvature of closed curves, J. Differential Geom. 20 (1984), no. 1, 1-22. https://doi.org/10.4310/jdg/1214438990
  11. E. Loubeau and S. Montaldo, Biminimal immersions, Proc. Edinb. Math. Soc. (2) 51 (2008), no. 2, 421-437.
  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. H. Urakawa, Calculus of Variation and Harmonic Maps, Transl. Math. Monograph. 132, Amer. Math. Soc., Providence, 1993.

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