Biminimal Curves in Euclidean Spaces

Kadri Aslan; Yılmaz Aydın; Günay Öztürk; Hassan Ugail

Araştırma Makalesi

Biminimal Curves in Euclidean Spaces

Yıl 2009, Cilt: 2 Sayı: 2, 46 - 52, 30.10.2009

Kadri Aslan , Yılmaz Aydın Günay Öztürk , Hassan Ugail

Öz

Anahtar Kelimeler

Biharmonic curve, Biminimal curve, curves of AW(k) type

Kaynakça

[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.

Yıl 2009, Cilt: 2 Sayı: 2, 46 - 52, 30.10.2009

Kadri Aslan , Yılmaz Aydın Günay Öztürk , Hassan Ugail

Öz

Kaynakça

[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.

Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Araştırma Makalesi
Yazarlar	Kadri Aslan Yılmaz Aydın Bu kişi benim Günay Öztürk Hassan Ugail
Yayımlanma Tarihi	30 Ekim 2009
Yayımlandığı Sayı	Yıl 2009 Cilt: 2 Sayı: 2

Kaynak Göster

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. Ekim 2009;2(2):46-52.
Chicago	Aslan, Kadri, Yılmaz Aydın, Günay Öztürk, ve Hassan Ugail. “Biminimal Curves in Euclidean Spaces”. International Electronic Journal of Geometry 2, sy. 2 (Ekim 2009): 46-52.
EndNote	Aslan K, Aydın Y, Öztürk G, Ugail H (01 Ekim 2009) Biminimal Curves in Euclidean Spaces. International Electronic Journal of Geometry 2 2 46–52.
IEEE	K. Aslan, Y. Aydın, G. Öztürk, ve H. Ugail, “Biminimal Curves in Euclidean Spaces”, Int. Electron. J. Geom., c. 2, sy. 2, ss. 46–52, 2009.
ISNAD	Aslan, Kadri vd. “Biminimal Curves in Euclidean Spaces”. International Electronic Journal of Geometry 2/2 (Ekim 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 vd. “Biminimal Curves in Euclidean Spaces”. International Electronic Journal of Geometry, c. 2, sy. 2, 2009, ss. 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.