Biminimal Curves in Euclidean Spaces

___

  • [1] K. Arslan and A. West, Product submanifolds with pointwise 3-planar normal sections, Glas- gow Math. J., 37 (1995), No 1, 73-81
  • [2] K. Arslan and C. O¨ zgu¨r, Curves of AW(k) type, Geometry and Topology of Submanifolds IX (Valanciennes/Lyon/Leuven, 1997), 21-26, World Sci. Publishing, River edge, (1999).
  • [3] M. Barros, O.J. Garay, On submanifolds with harmonic mean curvature, Proc. Amer. Math. Soc. 28 (1995), 2545-2549.
  • [4] R. Caddeo, S. Montaldo and D. Piu , Biharmonic curves and surfaces, Ren. d. Mat. serie VII, Roma, 21 (2001), 143-157.
  • [5] B.Y. Chen, Some open problems and conjecture on submanifolds of finite type, Schoow J. Math., 17 (1991), 164-188.
  • [6] J. Eells, J.H. Sampson. Harmonic mappings of Riemannian manifolds, Amer. J. Math, 86 (1964), 109-160.
  • [7] A. Gray, Modern differential geometry of curves and surfaces, Crc Press, 1993.
  • [8] G.Y. Jiang , 2-harmonic maps and first and second variation formulas, Chinese Ann. Math. Ser. A, 7 (1986), 386-401.
  • [9] B. Kılı¸c and K. Arslan, On curves and surfaces of AW(k) type, BAU¨ Fen Bil. Enst. Der., 6.1 (2004), 52-61.
  • [10] B. Kılıç, Finite type curves and surfaces, PhD. Thesis, Hacettepe U¨ niversitesi Fen Bil. Enst., (2002).
  • [11] B. Kilic, K. Arslan and G. Ozturk, Tangentially cubic curves in Euclidean spaces, Diff. Geo. and Dyn. Syst., 10 (2008),
  • [12] D. Langwitz, Differential and Riemannian Geometry, Academic press, 1965.
  • [13] L. Loubeau and S. Montaldo, Biminimal immersions in space forms, ArXiv:math.DGl 0405320.
  • [14] L. Loubeau and S. Montaldo, Biminimal immersions, ArXiv:math.DGl 0405320.
  • [15] Ü. Lümiste, Small dimensional irreducible submanifolds with parallel third fundamental form, Tartu Ülikooli Toimetised, Acta et comm. uni. Taruensis, 734 (1986), 50-62.
  • [16] C. Özgür, F. Gezgin, On some curves of AW(k) type, Diff. Geo. and Dyn. Syst. 7 (2005), 74-80.
  • [17] H. Pottman and M. Hofer, A variational approach to spline curves on Surfaces, Computer Aided Geometric Design, 22 (2005), 693-709.
  • [18] E. Salkowski, Zur Transformation von Raunkurven, Math. Ann. 66 (1909), 517-557.