Araştırma Makalesi
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Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space

Yıl 2019, Cilt: 12 Sayı: 2, 229 - 240, 03.10.2019

Bülent Altunkaya

https://doi.org/10.36890/iejg.585408

Öz

In this work, we study slant helices in the n-dimensional Euclidean space. We give  methods to determine the position vectors of slant helices from arclength parameterized curves that lie on the unit hypersphere. By means of these methods, first we characterize  slant helices and Salkowski curves which lie on 2n-dimensional hyperboloid. After that,  we characterize  rectifying slant helices which are geodesics of 2n-dimensional cone.

Anahtar Kelimeler

Slant helix Salkowski curve rectifying curve hyperspherical curve geodesic of a hypersurface

Kaynakça

  • [1] Ahmad TA, Turgut M. Some characterizations of slant helices in the Euclidean space En. Hac J Math Sta 2010; 39: 327-336.
  • [2] Arslan K, Celik Y, Deszcz C, Ozgur C. Submanifolds all of whose normal sections are W-curves. Far East J Math Sci 1997; 5: 537-544.
  • [3] Altunkaya B, Aksoyak FK, Kula L, Aytekin C. On rectifying slant helices in Euclidean 3-space. Kon J Math 2016; 4: 17-24.
  • [4] Altunkaya B, Kula L. General helices that lie on the sphere S2n in Euclidean space E2n+1. Uni J Math App 2018; 1: 166-170.
  • [5] Camci C, Ilarslan K, Kula L, Hacisalihoglu HH. Harmonic cuvature and general helices, Chaos Solitons Fractals 2009; 40: 2590-2596.
  • [6] Cambie S, Goemans W, Van Den Bussche I. Rectifying curves in the n-dimensional Euclidean space, Turkish J Math 2016; 40: 210-223.
  • [7] Chen BY. When does the position vector of a space curve always lie in its rectifying plane?, Amer Math Monthly 2003; 110: 147-152.
  • [8] Chen BY, Dillen F. Rectifying curves as centrodes and extremal curves. Bull Inst Math Aca Sinica 2005; 33: 77-90.
  • [9] Chen BY. Differential geometry of rectifying submanifolds. Int Elec J Geo 2016; 9: 1-8.
  • [10] Chen BY. Rectifying curves and geodesics on a cone in the Euclidean 3-space. Tamkang J Math 2017; 48: 209-214.
  • [11] Deshmukh S, Chen BY, Alshammari, SH. On rectifying curves in Euclidean 3-space. Turkish J Math 2017; 42: 609-620.
  • [12] Gluck H. Higher curvatures of curves in Euclidean space, Amer Math Monthly 1966; 73: 699-704.
  • [13] Ilarslan K, Nesovic E. Some characterizations of rectifying curves in Euclidean space E4, Turkish J Math 2008; 32:21-30.
  • [14] Izumiya S, Takeuchi N. New special curves and developable surfaces. Turkish J Math 2004; 28: 153-163.
  • [15] Izumiya S, Takeuchi N. Generic properties of helices and Bertrand curves. J Geom 2002; 74: 97-109.
  • [16] Kula L, Yaylı Y. On slant helix and its spherical indicatrix. App Math Comp 2005; 169: 600-607.
  • [17] Kula L, Ekmekci N, Yaylı Y, Ilarslan K. Characterizations of slant helices in Euclidean 3-space. Turkish J Math 2010; 34: 261-273.
  • [18] Lucas P, Ortega-Yagues JA. Rectifying curves in the three-dimensional sphere. J Math Anal Appl 2015; 421: 1855–1868.
  • [19] Monterde J. Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion. Com Aided Geo Design2009; 26(3): 271-278.
  • [20] O’Neill B. Elementary Differential Geometry. London, UK: Academic Press Inc, 2006.
  • [21] Salkowski, E. Zur transformation von raumkurven. Mathematische Annalen 1909; 66(4); 517-557.
  • [22] Yayli Y, Ziplar E. On slant helices and general helices in Euclidean n-space. Mathematica Aeterna 2011; 1: 599-610.
  • [23] Yayli Y, Gok I, Hacisalihoglu HH. Extended rectifying curves as new kind of modified Darboux vectors. TWMS J Pure Appl Math 2018;9: 18-31.

Yıl 2019, Cilt: 12 Sayı: 2, 229 - 240, 03.10.2019

Bülent Altunkaya

https://doi.org/10.36890/iejg.585408

Öz

Kaynakça

  • [1] Ahmad TA, Turgut M. Some characterizations of slant helices in the Euclidean space En. Hac J Math Sta 2010; 39: 327-336.
  • [2] Arslan K, Celik Y, Deszcz C, Ozgur C. Submanifolds all of whose normal sections are W-curves. Far East J Math Sci 1997; 5: 537-544.
  • [3] Altunkaya B, Aksoyak FK, Kula L, Aytekin C. On rectifying slant helices in Euclidean 3-space. Kon J Math 2016; 4: 17-24.
  • [4] Altunkaya B, Kula L. General helices that lie on the sphere S2n in Euclidean space E2n+1. Uni J Math App 2018; 1: 166-170.
  • [5] Camci C, Ilarslan K, Kula L, Hacisalihoglu HH. Harmonic cuvature and general helices, Chaos Solitons Fractals 2009; 40: 2590-2596.
  • [6] Cambie S, Goemans W, Van Den Bussche I. Rectifying curves in the n-dimensional Euclidean space, Turkish J Math 2016; 40: 210-223.
  • [7] Chen BY. When does the position vector of a space curve always lie in its rectifying plane?, Amer Math Monthly 2003; 110: 147-152.
  • [8] Chen BY, Dillen F. Rectifying curves as centrodes and extremal curves. Bull Inst Math Aca Sinica 2005; 33: 77-90.
  • [9] Chen BY. Differential geometry of rectifying submanifolds. Int Elec J Geo 2016; 9: 1-8.
  • [10] Chen BY. Rectifying curves and geodesics on a cone in the Euclidean 3-space. Tamkang J Math 2017; 48: 209-214.
  • [11] Deshmukh S, Chen BY, Alshammari, SH. On rectifying curves in Euclidean 3-space. Turkish J Math 2017; 42: 609-620.
  • [12] Gluck H. Higher curvatures of curves in Euclidean space, Amer Math Monthly 1966; 73: 699-704.
  • [13] Ilarslan K, Nesovic E. Some characterizations of rectifying curves in Euclidean space E4, Turkish J Math 2008; 32:21-30.
  • [14] Izumiya S, Takeuchi N. New special curves and developable surfaces. Turkish J Math 2004; 28: 153-163.
  • [15] Izumiya S, Takeuchi N. Generic properties of helices and Bertrand curves. J Geom 2002; 74: 97-109.
  • [16] Kula L, Yaylı Y. On slant helix and its spherical indicatrix. App Math Comp 2005; 169: 600-607.
  • [17] Kula L, Ekmekci N, Yaylı Y, Ilarslan K. Characterizations of slant helices in Euclidean 3-space. Turkish J Math 2010; 34: 261-273.
  • [18] Lucas P, Ortega-Yagues JA. Rectifying curves in the three-dimensional sphere. J Math Anal Appl 2015; 421: 1855–1868.
  • [19] Monterde J. Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion. Com Aided Geo Design2009; 26(3): 271-278.
  • [20] O’Neill B. Elementary Differential Geometry. London, UK: Academic Press Inc, 2006.
  • [21] Salkowski, E. Zur transformation von raumkurven. Mathematische Annalen 1909; 66(4); 517-557.
  • [22] Yayli Y, Ziplar E. On slant helices and general helices in Euclidean n-space. Mathematica Aeterna 2011; 1: 599-610.
  • [23] Yayli Y, Gok I, Hacisalihoglu HH. Extended rectifying curves as new kind of modified Darboux vectors. TWMS J Pure Appl Math 2018;9: 18-31.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Bülent Altunkaya 0000-0002-3186-5643

Yayımlanma Tarihi 3 Ekim 2019
Kabul Tarihi 10 Ağustos 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 2

Kaynak Göster

APA Altunkaya, B. (2019). Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. International Electronic Journal of Geometry, 12(2), 229-240. https://doi.org/10.36890/iejg.585408
AMA Altunkaya B. Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. Int. Electron. J. Geom. Ekim 2019;12(2):229-240. doi:10.36890/iejg.585408
Chicago Altunkaya, Bülent. “Slant Helices That Constructed from Hyperspherical Curves in the N-Dimensional Euclidean Space”. International Electronic Journal of Geometry 12, sy. 2 (Ekim 2019): 229-40. https://doi.org/10.36890/iejg.585408.
EndNote Altunkaya B (01 Ekim 2019) Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. International Electronic Journal of Geometry 12 2 229–240.
IEEE B. Altunkaya, “Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space”, Int. Electron. J. Geom., c. 12, sy. 2, ss. 229–240, 2019, doi: 10.36890/iejg.585408.
ISNAD Altunkaya, Bülent. “Slant Helices That Constructed from Hyperspherical Curves in the N-Dimensional Euclidean Space”. International Electronic Journal of Geometry 12/2 (Ekim 2019), 229-240. https://doi.org/10.36890/iejg.585408.
JAMA Altunkaya B. Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. Int. Electron. J. Geom. 2019;12:229–240.
MLA Altunkaya, Bülent. “Slant Helices That Constructed from Hyperspherical Curves in the N-Dimensional Euclidean Space”. International Electronic Journal of Geometry, c. 12, sy. 2, 2019, ss. 229-40, doi:10.36890/iejg.585408.
Vancouver Altunkaya B. Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. Int. Electron. J. Geom. 2019;12(2):229-40.
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