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Year 2020, Volume: 69 Issue: 1, 900 - 909, 30.06.2020

Beyhan Yılmaz Aykut Has

https://doi.org/10.31801/cfsuasmas.538177
Cited By: 1

Abstract

References

  • Babaarslan, M. and Yayli, Y., On helices and Bertrand curves in Euclidean 3-space, Mathematical and Computational Applications, 18(1)(2013) 1-11.
  • Cheng, Y.M. and Lin, C.C., On the generalized Bertrand curves in Euclidean N-spaces, Note di Matematica, 29(2)(2009) 33-39.
  • Izumiya, S. and Takeuchi, N., Generic properties of helices and Bertrand curves, J. Geom. 74 (2002), 97-109.
  • Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turk J Math. 28 (2004), 153-163.
  • Liu, H. and Wang, F., Mannheim partner curves in 3-space, J. Geom. 88 (2008), 120-126.
  • Matsuda, H. and Yorozu, S., Notes on Bertrand curves, Yokohama Mathematical Journal, 50(2003) 41-58.
  • Struik, D.J., Lectures on Classical Di¤erential Geometry, Dover Publications, 1988.
  • Uzunoğlu, B., Gök, ·I. and Yayli, Y., A new approach on curves of constant precession, Appl. Math. Comput. 275 (2016), 317-323.
  • Wang, F. and Liu, H., Mannheim partner curves in 3-Euclidean space, Math.Pract. Theory. 37 (2007), 141-143.
  • Whittemore, J.K., Bertrand curves and helices, Duke Math. J. 6 (1940), 235-245.
  • Zhao, W., Pei, D. and Cao, X., Mannheim curves in nonflat 3-Dimensional Space Forms, Adv. Math. Phys. 2015 (2015), 1-9.

Alternative partner curves in the Euclidean 3-space

Year 2020, Volume: 69 Issue: 1, 900 - 909, 30.06.2020

Beyhan Yılmaz Aykut Has

https://doi.org/10.31801/cfsuasmas.538177
Cited By: 1

Abstract

In the present paper, a new type of special curve couple which are called WC^{∗}-partner curves are introduced according to alternative moving frame {N,C,W}. The distance function between the corresponding points of reference curve and its partner curve is obtained. Besides, the angle function between the vector fields of alternative frame of the curves is expressed by means of alternative curvatures f and g. In addition to these, various characterizations are obtained related to these curves.

Keywords

Slant Helix alternative frame curve pairs

References

  • Babaarslan, M. and Yayli, Y., On helices and Bertrand curves in Euclidean 3-space, Mathematical and Computational Applications, 18(1)(2013) 1-11.
  • Cheng, Y.M. and Lin, C.C., On the generalized Bertrand curves in Euclidean N-spaces, Note di Matematica, 29(2)(2009) 33-39.
  • Izumiya, S. and Takeuchi, N., Generic properties of helices and Bertrand curves, J. Geom. 74 (2002), 97-109.
  • Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turk J Math. 28 (2004), 153-163.
  • Liu, H. and Wang, F., Mannheim partner curves in 3-space, J. Geom. 88 (2008), 120-126.
  • Matsuda, H. and Yorozu, S., Notes on Bertrand curves, Yokohama Mathematical Journal, 50(2003) 41-58.
  • Struik, D.J., Lectures on Classical Di¤erential Geometry, Dover Publications, 1988.
  • Uzunoğlu, B., Gök, ·I. and Yayli, Y., A new approach on curves of constant precession, Appl. Math. Comput. 275 (2016), 317-323.
  • Wang, F. and Liu, H., Mannheim partner curves in 3-Euclidean space, Math.Pract. Theory. 37 (2007), 141-143.
  • Whittemore, J.K., Bertrand curves and helices, Duke Math. J. 6 (1940), 235-245.
  • Zhao, W., Pei, D. and Cao, X., Mannheim curves in nonflat 3-Dimensional Space Forms, Adv. Math. Phys. 2015 (2015), 1-9.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Beyhan Yılmaz 0000-0002-5091-3487

Aykut Has 0000-0003-0658-9365

Publication Date June 30, 2020
Submission Date March 11, 2019
Acceptance Date February 25, 2020
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Yılmaz, B., & Has, A. (2020). Alternative partner curves in the Euclidean 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 900-909. https://doi.org/10.31801/cfsuasmas.538177
AMA Yılmaz B, Has A. Alternative partner curves in the Euclidean 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):900-909. doi:10.31801/cfsuasmas.538177
Chicago Yılmaz, Beyhan, and Aykut Has. “Alternative Partner Curves in the Euclidean 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 900-909. https://doi.org/10.31801/cfsuasmas.538177.
EndNote Yılmaz B, Has A (June 1, 2020) Alternative partner curves in the Euclidean 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 900–909.
IEEE B. Yılmaz and A. Has, “Alternative partner curves in the Euclidean 3-space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 900–909, 2020, doi: 10.31801/cfsuasmas.538177.
ISNAD Yılmaz, Beyhan - Has, Aykut. “Alternative Partner Curves in the Euclidean 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 900-909. https://doi.org/10.31801/cfsuasmas.538177.
JAMA Yılmaz B, Has A. Alternative partner curves in the Euclidean 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:900–909.
MLA Yılmaz, Beyhan and Aykut Has. “Alternative Partner Curves in the Euclidean 3-Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 900-9, doi:10.31801/cfsuasmas.538177.
Vancouver Yılmaz B, Has A. Alternative partner curves in the Euclidean 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):900-9.

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https://doi.org/10.31801/cfsuasmas.1026359

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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