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Differential Equations for a Space Curve According to the Unit Darboux Vector

Yıl 2018, Cilt: 9, 91 - 97, 28.12.2018

Öz

In this work, the differential equation of a differentiable curve is expressed, by making use of Laplace and normal Laplace operators, as a linear combination of the unit Darboux vector defined as C = sinφT + cosφB  of that curve. Later, the necessary and sufficient conditions are given for the space curves to be a 1-type Darboux vector.

Kaynakça

  • Alfred, G., Modern Differential Geometry of Curves and Surfaces with Mathematica, Boca Raton, Florida, USA: 2nd ed, CRC Press, 1997.
  • Arslan, K., Kocayigit, H., Onder, M., Characterizations of space curves with 1-type Darboux instantaneous rotation vector, CommunKorean Math. Soc., 31(2)(2016), 379–388.
  • Chen, B.Y., Ishikawa, S., Biharmonic surface in pseudo-Euclidean spaces, Mem Fac Sci Kyushu Univ Ser A, 45(2)(1991), 323–347.
  • Fenchel, W., On the differential geometry of closed space curves, Bull Amer Math Soc, 57(1951), 44–54.
  • Ferrandez, A., Lucas, P., Merano, MA., Biharmonic Hopf cylinders, Rocky Mountain J of Math, 28(3)(1998), 957–975.
  • Ferus, D., Schirrmacher, S., Submanifolds in Euclidean space with simple geodesics, Math Ann., 260(1982), 57–62.
  • Kocayigit, H., Hacisalihoglu, H.H., 1-type and biharmonic Frenet curves in Lorentzian 3-space, Iran J Sci Tech Trans A Sci, 33(2)(2009),159-168.
  • Kocayigit, H., Hacisalihoglu, H.H., 1-type and biharmonic curves in Euclidean 3-space, Int Electron J Geom, 4(1)(2011), 97–101.
  • Struik, D.J., Lectures on Classical Differential Geometry, Dover, GB: 2nd ed, Addison Wesley, 1988.
Yıl 2018, Cilt: 9, 91 - 97, 28.12.2018

Öz

Kaynakça

  • Alfred, G., Modern Differential Geometry of Curves and Surfaces with Mathematica, Boca Raton, Florida, USA: 2nd ed, CRC Press, 1997.
  • Arslan, K., Kocayigit, H., Onder, M., Characterizations of space curves with 1-type Darboux instantaneous rotation vector, CommunKorean Math. Soc., 31(2)(2016), 379–388.
  • Chen, B.Y., Ishikawa, S., Biharmonic surface in pseudo-Euclidean spaces, Mem Fac Sci Kyushu Univ Ser A, 45(2)(1991), 323–347.
  • Fenchel, W., On the differential geometry of closed space curves, Bull Amer Math Soc, 57(1951), 44–54.
  • Ferrandez, A., Lucas, P., Merano, MA., Biharmonic Hopf cylinders, Rocky Mountain J of Math, 28(3)(1998), 957–975.
  • Ferus, D., Schirrmacher, S., Submanifolds in Euclidean space with simple geodesics, Math Ann., 260(1982), 57–62.
  • Kocayigit, H., Hacisalihoglu, H.H., 1-type and biharmonic Frenet curves in Lorentzian 3-space, Iran J Sci Tech Trans A Sci, 33(2)(2009),159-168.
  • Kocayigit, H., Hacisalihoglu, H.H., 1-type and biharmonic curves in Euclidean 3-space, Int Electron J Geom, 4(1)(2011), 97–101.
  • Struik, D.J., Lectures on Classical Differential Geometry, Dover, GB: 2nd ed, Addison Wesley, 1988.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Süleyman Şenyurt 0000-0003-1097-5541

Osman Çakır

Yayımlanma Tarihi 28 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 9

Kaynak Göster

APA Şenyurt, S., & Çakır, O. (2018). Differential Equations for a Space Curve According to the Unit Darboux Vector. Turkish Journal of Mathematics and Computer Science, 9, 91-97.
AMA Şenyurt S, Çakır O. Differential Equations for a Space Curve According to the Unit Darboux Vector. TJMCS. Aralık 2018;9:91-97.
Chicago Şenyurt, Süleyman, ve Osman Çakır. “Differential Equations for a Space Curve According to the Unit Darboux Vector”. Turkish Journal of Mathematics and Computer Science 9, Aralık (Aralık 2018): 91-97.
EndNote Şenyurt S, Çakır O (01 Aralık 2018) Differential Equations for a Space Curve According to the Unit Darboux Vector. Turkish Journal of Mathematics and Computer Science 9 91–97.
IEEE S. Şenyurt ve O. Çakır, “Differential Equations for a Space Curve According to the Unit Darboux Vector”, TJMCS, c. 9, ss. 91–97, 2018.
ISNAD Şenyurt, Süleyman - Çakır, Osman. “Differential Equations for a Space Curve According to the Unit Darboux Vector”. Turkish Journal of Mathematics and Computer Science 9 (Aralık 2018), 91-97.
JAMA Şenyurt S, Çakır O. Differential Equations for a Space Curve According to the Unit Darboux Vector. TJMCS. 2018;9:91–97.
MLA Şenyurt, Süleyman ve Osman Çakır. “Differential Equations for a Space Curve According to the Unit Darboux Vector”. Turkish Journal of Mathematics and Computer Science, c. 9, 2018, ss. 91-97.
Vancouver Şenyurt S, Çakır O. Differential Equations for a Space Curve According to the Unit Darboux Vector. TJMCS. 2018;9:91-7.