Research Article
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Biminimal Curves in Euclidean Spaces

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

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.

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

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.

Details

Primary Language English
Journal Section Research Article
Authors

Kadri ASLAN>


Yılmaz AYDIN This is me


Günay ÖZTÜRK>


Hassan UGAİL>

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

Cite

Bibtex @research article { iejg598996, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2009}, volume = {2}, number = {2}, pages = {46 - 52}, title = {Biminimal Curves in Euclidean Spaces}, key = {cite}, author = {Aslan, Kadri and Aydın, Yılmaz and Öztürk, Günay and Ugail, Hassan} }
APA Aslan, K. , Aydın, Y. , Öztürk, G. & Ugail, H. (2009). Biminimal Curves in Euclidean Spaces . International Electronic Journal of Geometry , 2 (2) , 46-52 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/47444/598996
MLA Aslan, K. , Aydın, Y. , Öztürk, G. , Ugail, H. "Biminimal Curves in Euclidean Spaces" . International Electronic Journal of Geometry 2 (2009 ): 46-52 <https://dergipark.org.tr/en/pub/iejg/issue/47444/598996>
Chicago Aslan, K. , Aydın, Y. , Öztürk, G. , Ugail, H. "Biminimal Curves in Euclidean Spaces". International Electronic Journal of Geometry 2 (2009 ): 46-52
RIS TY - JOUR T1 - Biminimal Curves in Euclidean Spaces AU - KadriAslan, YılmazAydın, GünayÖztürk, HassanUgail Y1 - 2009 PY - 2009 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 46 EP - 52 VL - 2 IS - 2 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry Biminimal Curves in Euclidean Spaces %A Kadri Aslan , Yılmaz Aydın , Günay Öztürk , Hassan Ugail %T Biminimal Curves in Euclidean Spaces %D 2009 %J International Electronic Journal of Geometry %P -1307-5624 %V 2 %N 2 %R %U
ISNAD Aslan, Kadri , Aydın, Yılmaz , Öztürk, Günay , Ugail, Hassan . "Biminimal Curves in Euclidean Spaces". International Electronic Journal of Geometry 2 / 2 (October 2009): 46-52 .
AMA Aslan K. , Aydın Y. , Öztürk G. , Ugail H. Biminimal Curves in Euclidean Spaces. Int. Electron. J. Geom.. 2009; 2(2): 46-52.
Vancouver Aslan K. , Aydın Y. , Öztürk G. , Ugail H. Biminimal Curves in Euclidean Spaces. International Electronic Journal of Geometry. 2009; 2(2): 46-52.
IEEE K. Aslan , Y. Aydın , G. Öztürk and H. Ugail , "Biminimal Curves in Euclidean Spaces", International Electronic Journal of Geometry, vol. 2, no. 2, pp. 46-52, Oct. 2009