Slant helices of (k, m)-type in 𝔼4

Münevver Yildirim Yilmaz; Mehmet Bektaş

doi:10.2478/ausm-2018-0031

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Slant helices of (k, m)-type in 𝔼4

Acta Universitatis Sapientiae, Mathematica

Volume 10 (2018): Issue 2 (December 2018)

By: Münevver Yildirim Yilmaz and Mehmet Bektaş

Open Access

|Mar 2019

Abstract

In the present work, we define new type slant helices called (k,m)-type and we conclude that there are no (1,k) type (1 ≤ k ≤ 4) slant helices. Also we obtain conditions for different type slant helices.

References

[1] A. T. Ali, M. Turgut, Some characterizations of slant helices in the Euclidean space En, Hacet. J. Math. Stat., 39 (3), (2010), 327–336.
Search in Google Scholar Back to article
[2] A. T. Ali, R. Lopez, M. Turgut, k–type partially null and pseudo null slant helices in Minkowski 4-space, Math. Commun., 17 (1) (2012), 93–103.
Search in Google Scholar Back to article
[3] H. Gluck, Higher curvature of curves in Euclidean space, Amer. Math. Monthly, 73 (1996), 699–704.10.1080/00029890.1966.11970818
Open DOI Search in Google Scholar Back to article
[4] I. Gök, O. Z. Okuyucu, T. Kahraman, H. H. & Hacisalihoglu, On the quaternionic B 2-slant helices in the Euclidean space E 4, Adv. in App. Cliff. Alg, 21 (4) (2011), 707–719.10.1007/s00006-011-0284-6
Open DOI Search in Google Scholar Back to article
[5] H. H. Hacisalihoglu, Diferensiyel Geometri, Inönü Üniversitesi Fenedebiyat Fakültesi Yayinlari (In Turkish), 1983.
Search in Google Scholar Back to article
[6] S. Izumiya, N. Takeuchi, New Special Curves and Developable Surfaces, Turk J Math, 28 (2004), 153–163.
Search in Google Scholar Back to article
[7] L. Kula, N. Ekmekci, Y. Yayli, K. Ilarslan, Characterizations of slant helices in Euclidean 3-space, Turkish J. Math. 33 (2009), 1–13.10.3906/mat-0809-17
Open DOI Search in Google Scholar Back to article
[8] L. Kula, Y. Yayli, On Slant helix and its spherical indicatrix, App. Math. and Comput., 169 (2005), 600–607.10.1016/j.amc.2004.09.078
Open DOI Search in Google Scholar Back to article
[9] R. S. Millman, G. D. Parker, Elements of differential geometry, Prentice-Hall Inc., Englewood Cliffs, N. J. USA, 1977.
Search in Google Scholar Back to article
[10] M. Onder, M. Kazaz, H. Kocayigit, O. Hand Kilic, B2-slant helix in Euclidean 4-space E4, Int. J. Cont. Math. Sci., 3 (29) (2008), 1433–1444.
Search in Google Scholar Back to article
[11] Z. Özdemir, I. Gök, F. N. Ekmekci, & Y. Yayli, A New Approach on Type-3 Slant Helix in E 4, Gen. Math. Notes, 28 (1) (2015), 40–49.
Search in Google Scholar Back to article
[12] A. Senol, E. Ziplar, Y. Yayli, I Gök, A new approach on helices in Euclidean n-space, Math. Commun., 18 (1), (2013), 241–256.
Search in Google Scholar Back to article
[13] M. Turgut, S. Yilmaz, Characterizations of some special helices in E⁴, Sci. Magna, 4 (1) (2008), 51–55.
Search in Google Scholar Back to article
[14] M. Turgut, & A. T. Ali, Some characterizations of special curves in the Euclidean space E4, Acta Univ. Sapientiae Math., 2 (1) (2010), 111–122.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/ausm-2018-0031 | Journal eISSN: 2066-7752

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Language: English

Page range: 395 - 401

Submitted on: Jun 22, 2017

Published online: Mar 4, 2019

Published in print: Dec 1, 2018

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

slant helices,

Serret-Frenet frame

MSC:

53C040,

53A05

Related subjects:

Mathematics,

General mathematics

© 2019 Münevver Yildirim Yilmaz, Mehmet Bektaş, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 10 (2018): Issue 2 (December 2018)