Research article

Non-null slant ruled surfaces

  • Received: 20 December 2018 Accepted: 02 April 2019 Published: 19 April 2019
  • MSC : 53A25, 53C50, 14J26

  • In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space $E_{1}^{3} $. We introduce some characterizations for a non-null ruled surface to be a slant ruled surface in $E_{1}^{3} $. Moreover, we obtain some corollaries which give the relationships between a non-null slant ruled surface and its striction line.

    Citation: Mehmet Önder. Non-null slant ruled surfaces[J]. AIMS Mathematics, 2019, 4(3): 384-396. doi: 10.3934/math.2019.3.384

    Related Papers:

  • In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space $E_{1}^{3} $. We introduce some characterizations for a non-null ruled surface to be a slant ruled surface in $E_{1}^{3} $. Moreover, we obtain some corollaries which give the relationships between a non-null slant ruled surface and its striction line.


    加载中


    [1] R. A. Abdel-Baky, Slant ruled surface in the Euclidean 3-space, Sci. Magna, 9 (2013), 107-112.
    [2] A. T. Ali and R. Lopez, Slant helices in Minkowski space $E_{1}^{3}$, J. Korean Math. Soc., 48 (2011) 159-167.
    [3] A. T. Ali and M. Turgut, Position vector of a time-like slant helix in Minkowski 3-space, J. Math. Anal. Appl., 365 (2010) 559-569.
    [4] A. T. Ali, Position vectors of slant helices in Euclidean 3-space, J. Egypt. Math. Soc., 20 (2012) 1-6.
    [5] M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc., 125 (1997) 1503-1509.
    [6] J. K. Beem and P. E. Ehrlich, Global Lorentzian Geometry, New York: Marcel Dekker, 1981.
    [7] N. Ekmekçi and H. H. Hacı}salihoğlu, On helices of a Lorentzian manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 45 (1996) 45-50.
    [8] A. Ferrandez, A. Gimenez and P. Lucas, Null helices in Lorentzian space forms, Int. J. Mod. Phys. A, 16 (2001) 4845-4863.
    [9] S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk. J. Math., 28 (2004) 153-163.
    [10] O. Kaya and M. Önder, Position vector of a developable $h$-slant ruled surface, TWMS J. App. Eng. Math., 7 (2017) 322-331.
    [11] O. Kaya and M. Önder, Position vector of a developable $q$-slant ruled surface, Korean J. Math., 26 (2018) 545-559.
    [12] E. Kasap and N. Kuruoğlu, The Bertrand offsets of ruled surfaces in $IR_{1}^{3}$, Acta Math. Vietnam., 31 (2006) 39-48.
    [13] H. Kocayiğit and M. Önder, Timelike curves of constant slope in Minkowski space $E_{1}^{4}$, J. Sci. Techn. Beykent Univ., 1 (2007) 311-318.
    [14] L. Kula and Y. Yaylı, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (2005) 600-607.
    [15] A. Küçük, On the developable timelike trajectory ruled surfaces in Lorentz 3-space $IR_{1}^{3}$, Appl. Math. Comput., 157 (2004) 483-489.
    [16] B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, London: Academic Press, 1983.
    [17] M. Önder, Similar ruled surfaces with variable transformations in Minkowski 3-space, TWMS J. App. Eng. Math., 5}(2) (2015) 219-230.
    [18] M. Önder, H. Kocayiğit and M. Kazaz, Spacelike helices in Minkowski 4-space $E_{1}^{4}$, Ann. Univ. Ferrara, 56 (2010) 335-343.
    [19] M. Önder and H. H. Uğurlu, Frenet frames and invariants of timelike ruled surfaces, Ain Shams Eng. J., 4 (2013) 507-513.
    [20] M. Önder and H. H. Uğurlu, On the developable Mannheim offsets of timelike ruled surfaces, Proc. Natl. Acad. Sci., India, Sect. A, 84 (2014) 541-548.
    [21] M. Önder and H. H. Uğurlu, Frenet frames and Frenet invariants of spacelike ruled surfaces, Dokuz Eylul Univ. Fac. Eng. J. Sci. Eng., 19 (2017) 712-722.
    [22] M. Önder and O. Kaya, Slant null scrolls in Minkowski 3-space $E_{1}^{3}$, Kuwait J. Sci., 43 (2016) 31-47.
    [23] M. Önder and O. Kaya, Characterizations of slant ruled surfaces in the Euclidean 3-space, Caspian J. Math. Sci., 6 (2017) 31-46.
    [24] M. Önder, Slant ruled surfaces, Trans. J. Pure Appl. Math., 1 (2018) 63-82.
    [25] D. J. Struik, Lectures on Classical Differential Geometry, 2 Eds., Dover: Addison Wesley, 1988.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2882) PDF downloads(664) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog