Araştırma Makalesi
BibTex RIS Kaynak Göster

ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES

Yıl 2015, Cilt: 3 Sayı: 2, 190 - 201, 01.10.2015

Öz

In this study, de nition of involute-evolute curves for semi-dual quaternionic curves in semi-dual spaces D42 known as dual split quaternion and D31 are given and also some well-known theorems for involute-evolute dual split quaternionic curves are obtained.

Kaynakça

  • [1] Bharathi, K. and Nagaraj, M. Quaternion valued function of a real variable Serret-Frenet formula, Indian Journal of Pure and Applied Mathematics 18: (1987), 507-511.
  • [2] Bilici, M. and C alskan, M., On the Involutes of the Spacelike Curve with a Timelike Binormal in Minkowski 3-Space, International Mathematical Forum, 4 no 31 (2009), 1497-1509.
  • [3] Blaschke, W., Diferensiyel Geometri Dersleri, _Istanbul Universitesi Yaynlar, 1949.
  • [4] Boyer, C., A History of Mathematics, New York: Wiley, 1968.
  • [5] Bukcu, B. and Karacan, M.K., On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3-space, Int. J. Math. Sciences, 2(5): (2007), 221-232.
  • [6] Clifford, W. K., Preliminary skecth of biquaternions, Proceedings of London Math. Soc. 4, (1873), 361-395.
  • [7] Çöken, A.C., Ekici, C., Kocayusufoglu, _I. and Gorgulu, A., Formulas for dual split quaternionic curves, Kuwait J. Sci. Eng.1A(36): (2009), 1-14
  • [8] Çöken, A.C. and Tuna, A., On the quaternionic inclined curves in the semi-Euclidean space E42 , Applied Mathematics and Computation 155(2): (2004), 373-389.
  • [9] do Carmo, M.P., Di erential Geometry of Curves and Surfaces, 1976.
  • [10] Hacsalihoglu, H. H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi, Fen- Edebiyat Fakultesi Yayinlari 2, 1983.
  • [11] Inoguchi, J., Timelike surfaces of constant mean curvature in Minkowski 3-space, Tokyo Journal of Mathematics 21(1): (1998), 141-152.
  • [12] Kecilioglu, O. and Gundogan, H., Dual split quaternions and motions in Lorentz space R31 , Far East Journal of Mathematical Sciences (FJMS) 24(3): (2007), 425-437.
  • [13] Kobayashi, S. and Nomizu, K., Foundations of di erential geometry, Vol. I, John Wiley Sons Inc. Lcccn: (1963), 63-19209.
  • [14] Kuhnel, W., Di erential Geometry, Curves-Surfaces-Manifolds, American Mathematical Society, 2002.
  • [15] Lopez, R., Di erential geometry of curves and surfaces in Lorentz-Minkowski space, Mini- Course taught at the Instituto de Matematica e Estatistica (IME-USP), University of Sao Paulo, Brasil, 2008.
  • [16] Nizamoglu, S., Surfaces reglees paralleles, Ege Univ. Fen Fak. Derg., 9 (Ser. A), (1986), 37-48.
  • [17] O'Neill, B., Semi Riemannian Geometry with Applications to Relativity, Academic Press, Inc. New York, 1983.
  • [18] O'Neill, B., Elementary Di erential Geometry, Academic Press, Inc. New York, 2006.
  • [19]  Ozylmaz, E. and Ylmaz, S., Involute-Evolute Curve Couples in the Euclidean 4-Space, Int. J. Open Problems Compt.Math., vol.2 No.2, (2009).
  • [20]  Ozdemir, M. and Ergin, A. A., Rotations with unit timelike quaternions in Minkowski 3-space, Journal of Geometry and Physics 56: (2006), 322-336.
  • [21] Sivridag, A._I., Gunes, R. and Keles, S., The Serret-Frenet formulae for dual-valued functions of a single real variable, Mechanism and Machine Theory 29: (1994), 749-754.
  • [22] Study, E., Geometrie der Dynamen, Leipzig, Teubner, 1903.
  • [23] Turgut, M. and Yilmaz,S., On The Frenet Frame and A Characterization of space-like Involute-Evolute Curve Couple in Minkowski Space-time, Int. Math. Forum 3(16): (2008), 793-801.
  • [24] Ugurlu, H.H. and C alskan , A., The study mapping for directed space-like and time-like line in Minkowski 3-space R31 , Mathematical and ComputationalApplications 1(2): (1996), 142-148.
  • [25] Veldkamp, G. R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mechanism and Machine Theory 11: (1976), 141-156.
  • [26] Willmore, T.J., Riemannian Geometry, Published in the United States by Oxford University Press Inc., Newyork, 1993.
Yıl 2015, Cilt: 3 Sayı: 2, 190 - 201, 01.10.2015

Öz

Kaynakça

  • [1] Bharathi, K. and Nagaraj, M. Quaternion valued function of a real variable Serret-Frenet formula, Indian Journal of Pure and Applied Mathematics 18: (1987), 507-511.
  • [2] Bilici, M. and C alskan, M., On the Involutes of the Spacelike Curve with a Timelike Binormal in Minkowski 3-Space, International Mathematical Forum, 4 no 31 (2009), 1497-1509.
  • [3] Blaschke, W., Diferensiyel Geometri Dersleri, _Istanbul Universitesi Yaynlar, 1949.
  • [4] Boyer, C., A History of Mathematics, New York: Wiley, 1968.
  • [5] Bukcu, B. and Karacan, M.K., On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3-space, Int. J. Math. Sciences, 2(5): (2007), 221-232.
  • [6] Clifford, W. K., Preliminary skecth of biquaternions, Proceedings of London Math. Soc. 4, (1873), 361-395.
  • [7] Çöken, A.C., Ekici, C., Kocayusufoglu, _I. and Gorgulu, A., Formulas for dual split quaternionic curves, Kuwait J. Sci. Eng.1A(36): (2009), 1-14
  • [8] Çöken, A.C. and Tuna, A., On the quaternionic inclined curves in the semi-Euclidean space E42 , Applied Mathematics and Computation 155(2): (2004), 373-389.
  • [9] do Carmo, M.P., Di erential Geometry of Curves and Surfaces, 1976.
  • [10] Hacsalihoglu, H. H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi, Fen- Edebiyat Fakultesi Yayinlari 2, 1983.
  • [11] Inoguchi, J., Timelike surfaces of constant mean curvature in Minkowski 3-space, Tokyo Journal of Mathematics 21(1): (1998), 141-152.
  • [12] Kecilioglu, O. and Gundogan, H., Dual split quaternions and motions in Lorentz space R31 , Far East Journal of Mathematical Sciences (FJMS) 24(3): (2007), 425-437.
  • [13] Kobayashi, S. and Nomizu, K., Foundations of di erential geometry, Vol. I, John Wiley Sons Inc. Lcccn: (1963), 63-19209.
  • [14] Kuhnel, W., Di erential Geometry, Curves-Surfaces-Manifolds, American Mathematical Society, 2002.
  • [15] Lopez, R., Di erential geometry of curves and surfaces in Lorentz-Minkowski space, Mini- Course taught at the Instituto de Matematica e Estatistica (IME-USP), University of Sao Paulo, Brasil, 2008.
  • [16] Nizamoglu, S., Surfaces reglees paralleles, Ege Univ. Fen Fak. Derg., 9 (Ser. A), (1986), 37-48.
  • [17] O'Neill, B., Semi Riemannian Geometry with Applications to Relativity, Academic Press, Inc. New York, 1983.
  • [18] O'Neill, B., Elementary Di erential Geometry, Academic Press, Inc. New York, 2006.
  • [19]  Ozylmaz, E. and Ylmaz, S., Involute-Evolute Curve Couples in the Euclidean 4-Space, Int. J. Open Problems Compt.Math., vol.2 No.2, (2009).
  • [20]  Ozdemir, M. and Ergin, A. A., Rotations with unit timelike quaternions in Minkowski 3-space, Journal of Geometry and Physics 56: (2006), 322-336.
  • [21] Sivridag, A._I., Gunes, R. and Keles, S., The Serret-Frenet formulae for dual-valued functions of a single real variable, Mechanism and Machine Theory 29: (1994), 749-754.
  • [22] Study, E., Geometrie der Dynamen, Leipzig, Teubner, 1903.
  • [23] Turgut, M. and Yilmaz,S., On The Frenet Frame and A Characterization of space-like Involute-Evolute Curve Couple in Minkowski Space-time, Int. Math. Forum 3(16): (2008), 793-801.
  • [24] Ugurlu, H.H. and C alskan , A., The study mapping for directed space-like and time-like line in Minkowski 3-space R31 , Mathematical and ComputationalApplications 1(2): (1996), 142-148.
  • [25] Veldkamp, G. R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mechanism and Machine Theory 11: (1976), 141-156.
  • [26] Willmore, T.J., Riemannian Geometry, Published in the United States by Oxford University Press Inc., Newyork, 1993.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Cumali Ekıcı

Hatice Tozak

Yayımlanma Tarihi 1 Ekim 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

APA Ekıcı, C., & Tozak, H. (2015). ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES. Konuralp Journal of Mathematics, 3(2), 190-201.
AMA Ekıcı C, Tozak H. ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES. Konuralp J. Math. Ekim 2015;3(2):190-201.
Chicago Ekıcı, Cumali, ve Hatice Tozak. “ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES”. Konuralp Journal of Mathematics 3, sy. 2 (Ekim 2015): 190-201.
EndNote Ekıcı C, Tozak H (01 Ekim 2015) ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES. Konuralp Journal of Mathematics 3 2 190–201.
IEEE C. Ekıcı ve H. Tozak, “ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES”, Konuralp J. Math., c. 3, sy. 2, ss. 190–201, 2015.
ISNAD Ekıcı, Cumali - Tozak, Hatice. “ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES”. Konuralp Journal of Mathematics 3/2 (Ekim 2015), 190-201.
JAMA Ekıcı C, Tozak H. ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES. Konuralp J. Math. 2015;3:190–201.
MLA Ekıcı, Cumali ve Hatice Tozak. “ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES”. Konuralp Journal of Mathematics, c. 3, sy. 2, 2015, ss. 190-01.
Vancouver Ekıcı C, Tozak H. ON THE INVOLUTES FOR DUAL SPLIT QUATERNIONIC CURVES. Konuralp J. Math. 2015;3(2):190-201.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.