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ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE

Yıl 2016, Cilt: 4 Sayı: 2, 17 - 24, 15.10.2016

Öz

In this paper, we study the position vector of rectifying slant helices in $E^3$. First, we have found the general equations of the curvature and the torsion of rectifying slant helices. After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.

Kaynakça

  • [1] Ali T. Ahmad, Position vectors of slant helices in Euclidean space E3, Journal of the Egyptian Mathematical Society Volume 20, Issue 1, Pages 1-6, April 2012.
  • [2] Chen, B. Y., When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110, 147-152, 2003.
  • [3] Chen, B. Y., Dillen, F. Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica 33, No. 2, 77-90, 2005.
  • [4] Izumiya S., Takeuchi N., New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
  • [5] S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves , J. Geom. 74, 97-109, 2002.
  • [6] Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169, 600-607, 2005.
  • [7] Kula, L.; Ekmekci, N. Yayl, Y. and Ilarslan, K., Characterizations of slant helices in Euclidean 3-space, Turkish J. Math. 34, no. 2, 261273, 2010.
  • [8] O'Neill B., Elementary Di erential Geometry, Academic Press, 2006.
  • [9] Struik D. J., Lectures on Classical Di erential Geometry, Dover, 1961.
Yıl 2016, Cilt: 4 Sayı: 2, 17 - 24, 15.10.2016

Öz

Kaynakça

  • [1] Ali T. Ahmad, Position vectors of slant helices in Euclidean space E3, Journal of the Egyptian Mathematical Society Volume 20, Issue 1, Pages 1-6, April 2012.
  • [2] Chen, B. Y., When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110, 147-152, 2003.
  • [3] Chen, B. Y., Dillen, F. Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica 33, No. 2, 77-90, 2005.
  • [4] Izumiya S., Takeuchi N., New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
  • [5] S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves , J. Geom. 74, 97-109, 2002.
  • [6] Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169, 600-607, 2005.
  • [7] Kula, L.; Ekmekci, N. Yayl, Y. and Ilarslan, K., Characterizations of slant helices in Euclidean 3-space, Turkish J. Math. 34, no. 2, 261273, 2010.
  • [8] O'Neill B., Elementary Di erential Geometry, Academic Press, 2006.
  • [9] Struik D. J., Lectures on Classical Di erential Geometry, Dover, 1961.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

Bülent Altunkaya

Ferdağ K. Aksoyak

Levent Kula

Cahit Aytekin

Yayımlanma Tarihi 15 Ekim 2016
Gönderilme Tarihi 3 Şubat 2015
Kabul Tarihi 6 Ocak 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Altunkaya, B., Aksoyak, F. K., Kula, L., Aytekin, C. (2016). ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE. Konuralp Journal of Mathematics, 4(2), 17-24.
AMA Altunkaya B, Aksoyak FK, Kula L, Aytekin C. ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE. Konuralp J. Math. Ekim 2016;4(2):17-24.
Chicago Altunkaya, Bülent, Ferdağ K. Aksoyak, Levent Kula, ve Cahit Aytekin. “ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE”. Konuralp Journal of Mathematics 4, sy. 2 (Ekim 2016): 17-24.
EndNote Altunkaya B, Aksoyak FK, Kula L, Aytekin C (01 Ekim 2016) ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE. Konuralp Journal of Mathematics 4 2 17–24.
IEEE B. Altunkaya, F. K. Aksoyak, L. Kula, ve C. Aytekin, “ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE”, Konuralp J. Math., c. 4, sy. 2, ss. 17–24, 2016.
ISNAD Altunkaya, Bülent vd. “ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE”. Konuralp Journal of Mathematics 4/2 (Ekim 2016), 17-24.
JAMA Altunkaya B, Aksoyak FK, Kula L, Aytekin C. ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE. Konuralp J. Math. 2016;4:17–24.
MLA Altunkaya, Bülent vd. “ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE”. Konuralp Journal of Mathematics, c. 4, sy. 2, 2016, ss. 17-24.
Vancouver Altunkaya B, Aksoyak FK, Kula L, Aytekin C. ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE. Konuralp J. Math. 2016;4(2):17-24.
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