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Biminimal Curves in Euclidean Spaces

Year 2009, Volume: 2 Issue: 2, 46 - 52, 30.10.2009

Kadri Aslan , Yılmaz Aydın Günay Öztürk , Hassan Ugail

Abstract



Keywords

Biharmonic curve Biminimal curve curves of AW(k) type

References

  • [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.

Year 2009, Volume: 2 Issue: 2, 46 - 52, 30.10.2009

Kadri Aslan , Yılmaz Aydın Günay Öztürk , Hassan Ugail

Abstract

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Kadri Aslan

Yılmaz Aydın This is me

Günay Öztürk

Hassan Ugail

Publication Date October 30, 2009
Published in Issue Year 2009 Volume: 2 Issue: 2

Cite

APA Aslan, K., Aydın, Y., Öztürk, G., Ugail, H. (2009). Biminimal Curves in Euclidean Spaces. International Electronic Journal of Geometry, 2(2), 46-52.
AMA Aslan K, Aydın Y, Öztürk G, Ugail H. Biminimal Curves in Euclidean Spaces. Int. Electron. J. Geom. October 2009;2(2):46-52.
Chicago Aslan, Kadri, Yılmaz Aydın, Günay Öztürk, and Hassan Ugail. “Biminimal Curves in Euclidean Spaces”. International Electronic Journal of Geometry 2, no. 2 (October 2009): 46-52.
EndNote Aslan K, Aydın Y, Öztürk G, Ugail H (October 1, 2009) Biminimal Curves in Euclidean Spaces. International Electronic Journal of Geometry 2 2 46–52.
IEEE K. Aslan, Y. Aydın, G. Öztürk, and H. Ugail, “Biminimal Curves in Euclidean Spaces”, Int. Electron. J. Geom., vol. 2, no. 2, pp. 46–52, 2009.
ISNAD Aslan, Kadri et al. “Biminimal Curves in Euclidean Spaces”. International Electronic Journal of Geometry 2/2 (October 2009), 46-52.
JAMA Aslan K, Aydın Y, Öztürk G, Ugail H. Biminimal Curves in Euclidean Spaces. Int. Electron. J. Geom. 2009;2:46–52.
MLA Aslan, Kadri et al. “Biminimal Curves in Euclidean Spaces”. International Electronic Journal of Geometry, vol. 2, no. 2, 2009, pp. 46-52.
Vancouver Aslan K, Aydın Y, Öztürk G, Ugail H. Biminimal Curves in Euclidean Spaces. Int. Electron. J. Geom. 2009;2(2):46-52.