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Year 2018, Volume: 1 Issue: 3, 166 - 170, 30.09.2018

Bülent Altunkaya Levent Kula

https://doi.org/10.32323/ujma.434361
Cited By: 4

Abstract

References

  • [1] Ali, Ahmad T., Turgut, M.: Some characterizations of slant helices in the Euclidean space En, Hacettepe Journal of Mathematics and Statistics, 39, 327-336, (2010).
  • [2] Breuer, S. and Gottlieb, D.: Explicit characterization of spherical curves, Proc. Am. Math. Soc., 274, 126–127, (1972).
  • [3] Camci, C. Ilarslan, K. Kula, L. and Hacisalihoglu, H.H.: Harmonic cuvature and general helices, Chaos Solitons & Fractals, 40, 2590-2596, (2009).
  • [4] Gluck, H.: Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699-704, (1966).
  • [5] Hayden, H. A.: On a general helix in a Riemannian n-space, Proc. London Math. Soc. 2, 37-45, (1931).
  • [6] Monterde, J.,: Curves with constant curvature ratios, Bol. Soc. Mat. Mexicana 3a, 13/1, 177–186, (2007).
  • [7] Romero-Fuster, M.C., Sanabria-Codesal, E.: Generalized helices, twistings and flattenings of curves in n-space. Mat. Cont., 17 , 267-280, (1999).
  • [8] Struik, D.J.: Lectures on Classical Differential Geometry, Dover, New-York, (1988).
  • [9] Wong Y.C.,: A global formulation of the condition for a curve to lie in a sphere, Monatsch Math, 67, 363–365, (1963).
  • [10] Wong Y.C.,: On a explicit characterization of spherical curves, Proc. Am. Math. Soc., 34, 239–242, (1972).

General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$

Year 2018, Volume: 1 Issue: 3, 166 - 170, 30.09.2018

Bülent Altunkaya Levent Kula

https://doi.org/10.32323/ujma.434361
Cited By: 4

Abstract

In this work, we give two methods to generate general helices that lie on the sphere  $S^{2n}$ in Euclidean (2n+1)-space $E^{2n+1}$.

Keywords

General helix sphere spherical curve

References

  • [1] Ali, Ahmad T., Turgut, M.: Some characterizations of slant helices in the Euclidean space En, Hacettepe Journal of Mathematics and Statistics, 39, 327-336, (2010).
  • [2] Breuer, S. and Gottlieb, D.: Explicit characterization of spherical curves, Proc. Am. Math. Soc., 274, 126–127, (1972).
  • [3] Camci, C. Ilarslan, K. Kula, L. and Hacisalihoglu, H.H.: Harmonic cuvature and general helices, Chaos Solitons & Fractals, 40, 2590-2596, (2009).
  • [4] Gluck, H.: Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699-704, (1966).
  • [5] Hayden, H. A.: On a general helix in a Riemannian n-space, Proc. London Math. Soc. 2, 37-45, (1931).
  • [6] Monterde, J.,: Curves with constant curvature ratios, Bol. Soc. Mat. Mexicana 3a, 13/1, 177–186, (2007).
  • [7] Romero-Fuster, M.C., Sanabria-Codesal, E.: Generalized helices, twistings and flattenings of curves in n-space. Mat. Cont., 17 , 267-280, (1999).
  • [8] Struik, D.J.: Lectures on Classical Differential Geometry, Dover, New-York, (1988).
  • [9] Wong Y.C.,: A global formulation of the condition for a curve to lie in a sphere, Monatsch Math, 67, 363–365, (1963).
  • [10] Wong Y.C.,: On a explicit characterization of spherical curves, Proc. Am. Math. Soc., 34, 239–242, (1972).
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Bülent Altunkaya

Levent Kula

Publication Date September 30, 2018
Submission Date June 18, 2018
Acceptance Date August 3, 2018
Published in Issue Year 2018 Volume: 1 Issue: 3

Cite

APA Altunkaya, B., & Kula, L. (2018). General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$. Universal Journal of Mathematics and Applications, 1(3), 166-170. https://doi.org/10.32323/ujma.434361
AMA Altunkaya B, Kula L. General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$. Univ. J. Math. Appl. September 2018;1(3):166-170. doi:10.32323/ujma.434361
Chicago Altunkaya, Bülent, and Levent Kula. “General Helices That Lie on the Sphere $S^{2n}$ in Euclidean Space $E^{2n+1}$”. Universal Journal of Mathematics and Applications 1, no. 3 (September 2018): 166-70. https://doi.org/10.32323/ujma.434361.
EndNote Altunkaya B, Kula L (September 1, 2018) General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$. Universal Journal of Mathematics and Applications 1 3 166–170.
IEEE B. Altunkaya and L. Kula, “General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 166–170, 2018, doi: 10.32323/ujma.434361.
ISNAD Altunkaya, Bülent - Kula, Levent. “General Helices That Lie on the Sphere $S^{2n}$ in Euclidean Space $E^{2n+1}$”. Universal Journal of Mathematics and Applications 1/3 (September 2018), 166-170. https://doi.org/10.32323/ujma.434361.
JAMA Altunkaya B, Kula L. General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$. Univ. J. Math. Appl. 2018;1:166–170.
MLA Altunkaya, Bülent and Levent Kula. “General Helices That Lie on the Sphere $S^{2n}$ in Euclidean Space $E^{2n+1}$”. Universal Journal of Mathematics and Applications, vol. 1, no. 3, 2018, pp. 166-70, doi:10.32323/ujma.434361.
Vancouver Altunkaya B, Kula L. General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$. Univ. J. Math. Appl. 2018;1(3):166-70.

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