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Some Characterizations of Slant Helices in the Euclidean Space En

Yıl 2010, Cilt: 39 Sayı: 3, 327 - 336, 01.03.2010

Öz

In this work, the notion of a slant helix is extended to the space En First, we introduce the type-2 harmonic curvatures of a regular curve.
Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some characterizations of slant helices in terms of type-2 harmonic curvatures.

Kaynakça

  • Ali, A. Inclined curves in the Euclidean 5-space E5, J. Advanced Research in Pure Math. (1), 15–22, 2009.
  • Ali, A. and L´opez, R. Slant helices in Minkowski space E1, preprint, 2008: arXiv: 1464v1 [math.DG].
  • Ali, A. and L´opez, R. Timelike B2-slant helices in Minkowski space E4, Archivum Math. (1), 39–46, 2010.
  • Ali, A. Position vetors of slant helices in Euclidean 3-space, preprint, 2009: arXiv: 0750v1 [math.DG].
  • Barros, M. General helices and a theorem of Lancert, Proc. Amer. Math. Soc. 125, 1503– , 1997.
  • Camcı, C¸ ., ˙Ilarslan, K., Kula, L. and Hacısaliho˘glu, H. H. Harmonic curvatures and gener- alized helices in En, Chaos, Solitons and Fractals 40, 2590–2596, 2009.
  • Ekmek¸ci, N., Hacisaliho˘glu, H. H. and ˙Ilarslan, K. Harmonic curvatures in Lorentzian space, Bull. Malaysian Math. Soc. (Second Series) 23 (2), 173–179, 2000.
  • Erdo˘gan, M. and Yılmaz, G. Null generalized and slant helices in 4-dimensional Lorentz- Minkowski space, Int. J. Contemp. Math. Sci. 3 (23), 1113–1120, 2008.
  • Gluck, H. Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699– , 1966.
  • Izumiya, S. and Takeuchi, N. New special curves and developable surfaces, Turk. J. Math. (2), 531–537, 2004.
  • Kula, L. and Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput. (1), 600ˆu-607, 2005.
  • Kula, L., Ekmek¸ci, N., Yayli Y. and ˙Ilarslan, K. Characterizations of slant helices in Eu- clidean 3-space, Turk. J. Math. 169 (1), 600ˆu-607, 2009.
  • Milman, R. S. and Parker, G. D. Elements of Differential Geometry (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1977).
  • Monterde, J. Curves with constant curvature ratios, Bull. Mexican Math. Soc. Ser. 3A (1), 177–186, 2007.
  • Monterde, J. Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. 26, 271–278, 2009.
  • ¨Onder, M., Kazaz, M., Kocayi˘git, H. and Kili¸c, O. B2-slant helix in Euclidean 4-space E4, Int. J. Contemp. Math. Sci. 3 (29), 1433–1440, 2008.
  • ¨Ozdamar, E. and Hacisaliho˘glu, H. H. A characterization of inclined curves in Euclidean n-space, Comm. Fac. Sci. Univ. Ankara, Ser. A1 24, 15–23, 1975.
  • ¨Ozt¨urk, G., Arslan, K. and Hacisalihoglu, H. H. A characterization of ccr-curves in Rm, Proc. Estonian Acad. Sci. 57 (4), 217–224, 2008.
  • Petrovic-Torgasev, M. and Sucurovic, E. W-curves in Minkowski spacetime, Novi. Sad. J. Math. 32 (2), 55–65, 2002.
  • Scofield, P. D. Curves of constant precession, Amer. Math. Monthly 102, 531–537, 1995.
  • Turgut, M. and Yilmaz, S. Characterizations of some special helices in E4, Sci. Magna. (1), 51–55, 2008.
  • Turgut, M. and Yilmaz, S. Some characterizations of type-3 slant helices in Minkowski space-time, Involve J. Math.2 (1), 115–120, 2009.

SOME CHARACTERIZATIONS OF SLANT HELICES IN THE EUCLIDEAN SPACE En

Yıl 2010, Cilt: 39 Sayı: 3, 327 - 336, 01.03.2010

Öz

Kaynakça

  • Ali, A. Inclined curves in the Euclidean 5-space E5, J. Advanced Research in Pure Math. (1), 15–22, 2009.
  • Ali, A. and L´opez, R. Slant helices in Minkowski space E1, preprint, 2008: arXiv: 1464v1 [math.DG].
  • Ali, A. and L´opez, R. Timelike B2-slant helices in Minkowski space E4, Archivum Math. (1), 39–46, 2010.
  • Ali, A. Position vetors of slant helices in Euclidean 3-space, preprint, 2009: arXiv: 0750v1 [math.DG].
  • Barros, M. General helices and a theorem of Lancert, Proc. Amer. Math. Soc. 125, 1503– , 1997.
  • Camcı, C¸ ., ˙Ilarslan, K., Kula, L. and Hacısaliho˘glu, H. H. Harmonic curvatures and gener- alized helices in En, Chaos, Solitons and Fractals 40, 2590–2596, 2009.
  • Ekmek¸ci, N., Hacisaliho˘glu, H. H. and ˙Ilarslan, K. Harmonic curvatures in Lorentzian space, Bull. Malaysian Math. Soc. (Second Series) 23 (2), 173–179, 2000.
  • Erdo˘gan, M. and Yılmaz, G. Null generalized and slant helices in 4-dimensional Lorentz- Minkowski space, Int. J. Contemp. Math. Sci. 3 (23), 1113–1120, 2008.
  • Gluck, H. Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699– , 1966.
  • Izumiya, S. and Takeuchi, N. New special curves and developable surfaces, Turk. J. Math. (2), 531–537, 2004.
  • Kula, L. and Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput. (1), 600ˆu-607, 2005.
  • Kula, L., Ekmek¸ci, N., Yayli Y. and ˙Ilarslan, K. Characterizations of slant helices in Eu- clidean 3-space, Turk. J. Math. 169 (1), 600ˆu-607, 2009.
  • Milman, R. S. and Parker, G. D. Elements of Differential Geometry (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1977).
  • Monterde, J. Curves with constant curvature ratios, Bull. Mexican Math. Soc. Ser. 3A (1), 177–186, 2007.
  • Monterde, J. Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. 26, 271–278, 2009.
  • ¨Onder, M., Kazaz, M., Kocayi˘git, H. and Kili¸c, O. B2-slant helix in Euclidean 4-space E4, Int. J. Contemp. Math. Sci. 3 (29), 1433–1440, 2008.
  • ¨Ozdamar, E. and Hacisaliho˘glu, H. H. A characterization of inclined curves in Euclidean n-space, Comm. Fac. Sci. Univ. Ankara, Ser. A1 24, 15–23, 1975.
  • ¨Ozt¨urk, G., Arslan, K. and Hacisalihoglu, H. H. A characterization of ccr-curves in Rm, Proc. Estonian Acad. Sci. 57 (4), 217–224, 2008.
  • Petrovic-Torgasev, M. and Sucurovic, E. W-curves in Minkowski spacetime, Novi. Sad. J. Math. 32 (2), 55–65, 2002.
  • Scofield, P. D. Curves of constant precession, Amer. Math. Monthly 102, 531–537, 1995.
  • Turgut, M. and Yilmaz, S. Characterizations of some special helices in E4, Sci. Magna. (1), 51–55, 2008.
  • Turgut, M. and Yilmaz, S. Some characterizations of type-3 slant helices in Minkowski space-time, Involve J. Math.2 (1), 115–120, 2009.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Matematik
Yazarlar

Ahmad T. Ali Bu kişi benim

Melih Turgut Bu kişi benim

Yayımlanma Tarihi 1 Mart 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 39 Sayı: 3

Kaynak Göster

APA Ali, A. T., & Turgut, M. (2010). Some Characterizations of Slant Helices in the Euclidean Space En. Hacettepe Journal of Mathematics and Statistics, 39(3), 327-336.
AMA Ali AT, Turgut M. Some Characterizations of Slant Helices in the Euclidean Space En. Hacettepe Journal of Mathematics and Statistics. Mart 2010;39(3):327-336.
Chicago Ali, Ahmad T., ve Melih Turgut. “Some Characterizations of Slant Helices in the Euclidean Space En”. Hacettepe Journal of Mathematics and Statistics 39, sy. 3 (Mart 2010): 327-36.
EndNote Ali AT, Turgut M (01 Mart 2010) Some Characterizations of Slant Helices in the Euclidean Space En. Hacettepe Journal of Mathematics and Statistics 39 3 327–336.
IEEE A. T. Ali ve M. Turgut, “Some Characterizations of Slant Helices in the Euclidean Space En”, Hacettepe Journal of Mathematics and Statistics, c. 39, sy. 3, ss. 327–336, 2010.
ISNAD Ali, Ahmad T. - Turgut, Melih. “Some Characterizations of Slant Helices in the Euclidean Space En”. Hacettepe Journal of Mathematics and Statistics 39/3 (Mart 2010), 327-336.
JAMA Ali AT, Turgut M. Some Characterizations of Slant Helices in the Euclidean Space En. Hacettepe Journal of Mathematics and Statistics. 2010;39:327–336.
MLA Ali, Ahmad T. ve Melih Turgut. “Some Characterizations of Slant Helices in the Euclidean Space En”. Hacettepe Journal of Mathematics and Statistics, c. 39, sy. 3, 2010, ss. 327-36.
Vancouver Ali AT, Turgut M. Some Characterizations of Slant Helices in the Euclidean Space En. Hacettepe Journal of Mathematics and Statistics. 2010;39(3):327-36.