Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space

Authors

  • Yılmaz TUNÇER Usak University
  • Serpil Ünal Usak University
  • Murat Kemal Karacan Usak University

DOI:

https://doi.org/10.5556/j.tkjm.51.2020.2946

Keywords:

Involute curve, Evolute curve, Helix, Slant helix, Spherical indicatrix.

Abstract

In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.

Author Biographies

Yılmaz TUNÇER, Usak University

Mathematics Department of Science and Art Faculty

Serpil Ünal, Usak University

Mathematics Department of Science and Art Faculty

Murat Kemal Karacan, Usak University

Mathematics Department of Science and Art Faculty

References

F.Wang and H. Liu, Mannheim Partner Curve in 3-Euclidean Space, Mat hematics in Practice and Theory, 37 (2007), 141-143.

H. Liu and F. Wang, Mannheim Partner Curve in 3-Space, Journal of Geometry, 88 (2008),120-126.

H. Matsuda and S. Yorozu, Notes on Bertrand Curves, Yokohama Math. J., 50 (2003), 41-58.

J. Monterde,Curves with constant curvature ratios, Bol. Soc. Math. Mexicana (3) 13, no.1 (2007),177-186.

L. Kula and Y. Yayli, On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169 (2005), 600-607.

L. Kula, N. Ekmekci, Y. Yayli and K. _Ilarslan, Characterizations of slant Helices in Euclidean 3-Space, Turk J. Math. 34 (2010), 261-273.

M.P. Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New Jersey, 1976.

S. Izumiya and N. Takeuchi, New Special Curves and Developable Surfaces, Turk. J. Math., 28 (2004), 153-164.

Additional Files

Published

2020-06-25

How to Cite

TUNÇER, Y., Ünal, S., & Karacan, M. K. (2020). Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space. Tamkang Journal of Mathematics, 51(2), 113-121. https://doi.org/10.5556/j.tkjm.51.2020.2946

Issue

Section

Papers