Alternative partner curves in the Euclidean 3-space

Yıl 2020, Cilt: 69 Sayı: 1, 900 - 909, 30.06.2020

Beyhan Yılmaz , Aykut Has

https://doi.org/10.31801/cfsuasmas.538177

Cited By: 3

Öz

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.

Anahtar Kelimeler

Slant Helix, alternative frame, curve pairs

Kaynakça

• 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.