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Year 2020, Volume: 5 Issue: 2, 63 - 72, 31.10.2020

Abstract

References

  • Çakır O.,Şenyurt, S. Harmonicity and Differential Equation of Involute of a Curve in E3. Thermal Science. 23(6), 2019, 2119–2125.
  • Boyer, C. A History of Mathematics, New York:Wiley. 1968, 334.
  • Bilici, M., Caliskan, M. On the involutes of the spacelike curve with a timelike binormal in Minkowski 3-space. International Mathematical Forum. 4(31), 2009, 1497–1509.
  • Şenyurt S., Cevahir C., Altun Y. On Spatial Quaternionic Involute Curve A New View. Advances in Clifford Algebras. 27(2), 2017, 1815–1824.
  • Kocayigit, H. and Hacisalihoglu H. H. 1-Type curves and biharmonic curves in Euclidean 3-space. Int. Elect. Journ. of Geo. 4(1), 2011 , 97–101.
  • Arslan, K., Kocayigit, H. and Onder, M. Characterizations of Space Curves with 1-type Darboux Instantaneous Rotation Vector. Commun. Korean Math. Soc. 31 (2), 2016, 379–388.
  • Chen, B. Y. And Ishikawa, S. Biharmonic Surface in Pseudo-Euclidean Spaces. Mem. Fac. Sci. Kyushu Univ. 45(1),1991 , 323–347.
  • Şenyurt, S. , Çakır O. Diferential Equations for a Space Curve According to the Unit Darboux Vector. Turk. J. Math. Comput. Sci. 9(1), 2018, 91–97.
  • Sabuncuoglu, A. Diferensiyel Geometri, Nobel Akademik Yayincilik, Ankara, 2014.
  • Fenchel, W. On The Differential Geometry of Closed Space Curves. Bulletin of the American Mathematical Society. 57, 1951, 44–54.
  • Şenyurt, S., Sivas, S., Çalışkan, A. N∗C∗-Smarandache Curves of Involute-Evolute Curve Couple According to Frenet Frame. Algebras, Groups and Geometries. 33(2), 2016, 153–163.
  • Kocayigit, H. , Önder M., Hacisalihoglu, H.H. Harmonic 1-type Curves andWeak Biharmonic Curves in Lorentzian 3-space. An Alele Stiintifice Ale Universitatii ”Al.I. Cuza” Din Iasi(S.N.) Matematica, Tomul LX. 60(1), 2014, 109–124.

Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method

Year 2020, Volume: 5 Issue: 2, 63 - 72, 31.10.2020

Abstract

In this study we first write the characterizations of involute of a curve by means of the unit Darboux vector of the involute curve. Then we make use of the Frenet formulas [1] to explain the characterizations of involute of a curve by means of Frenet apparatus of the main curve. Finally we examined the helix as an example.

References

  • Çakır O.,Şenyurt, S. Harmonicity and Differential Equation of Involute of a Curve in E3. Thermal Science. 23(6), 2019, 2119–2125.
  • Boyer, C. A History of Mathematics, New York:Wiley. 1968, 334.
  • Bilici, M., Caliskan, M. On the involutes of the spacelike curve with a timelike binormal in Minkowski 3-space. International Mathematical Forum. 4(31), 2009, 1497–1509.
  • Şenyurt S., Cevahir C., Altun Y. On Spatial Quaternionic Involute Curve A New View. Advances in Clifford Algebras. 27(2), 2017, 1815–1824.
  • Kocayigit, H. and Hacisalihoglu H. H. 1-Type curves and biharmonic curves in Euclidean 3-space. Int. Elect. Journ. of Geo. 4(1), 2011 , 97–101.
  • Arslan, K., Kocayigit, H. and Onder, M. Characterizations of Space Curves with 1-type Darboux Instantaneous Rotation Vector. Commun. Korean Math. Soc. 31 (2), 2016, 379–388.
  • Chen, B. Y. And Ishikawa, S. Biharmonic Surface in Pseudo-Euclidean Spaces. Mem. Fac. Sci. Kyushu Univ. 45(1),1991 , 323–347.
  • Şenyurt, S. , Çakır O. Diferential Equations for a Space Curve According to the Unit Darboux Vector. Turk. J. Math. Comput. Sci. 9(1), 2018, 91–97.
  • Sabuncuoglu, A. Diferensiyel Geometri, Nobel Akademik Yayincilik, Ankara, 2014.
  • Fenchel, W. On The Differential Geometry of Closed Space Curves. Bulletin of the American Mathematical Society. 57, 1951, 44–54.
  • Şenyurt, S., Sivas, S., Çalışkan, A. N∗C∗-Smarandache Curves of Involute-Evolute Curve Couple According to Frenet Frame. Algebras, Groups and Geometries. 33(2), 2016, 153–163.
  • Kocayigit, H. , Önder M., Hacisalihoglu, H.H. Harmonic 1-type Curves andWeak Biharmonic Curves in Lorentzian 3-space. An Alele Stiintifice Ale Universitatii ”Al.I. Cuza” Din Iasi(S.N.) Matematica, Tomul LX. 60(1), 2014, 109–124.
There are 12 citations in total.

Details

Primary Language English
Journal Section Volume V Issue II 2020
Authors

Süleyman ŞENYURT

Osman ÇAKIR 0000-0002-2664-5232

Publication Date October 31, 2020
Published in Issue Year 2020 Volume: 5 Issue: 2

Cite

APA ŞENYURT, S., & ÇAKIR, O. (2020). Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method. Turkish Journal of Science, 5(2), 63-72.
AMA ŞENYURT S, ÇAKIR O. Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method. TJOS. October 2020;5(2):63-72.
Chicago ŞENYURT, Süleyman, and Osman ÇAKIR. “Calculation of the Differential Equations and Harmonicity of the Involute Curve According to Unit Darboux Vector With a New Method”. Turkish Journal of Science 5, no. 2 (October 2020): 63-72.
EndNote ŞENYURT S, ÇAKIR O (October 1, 2020) Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method. Turkish Journal of Science 5 2 63–72.
IEEE S. ŞENYURT and O. ÇAKIR, “Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method”, TJOS, vol. 5, no. 2, pp. 63–72, 2020.
ISNAD ŞENYURT, Süleyman - ÇAKIR, Osman. “Calculation of the Differential Equations and Harmonicity of the Involute Curve According to Unit Darboux Vector With a New Method”. Turkish Journal of Science 5/2 (October 2020), 63-72.
JAMA ŞENYURT S, ÇAKIR O. Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method. TJOS. 2020;5:63–72.
MLA ŞENYURT, Süleyman and Osman ÇAKIR. “Calculation of the Differential Equations and Harmonicity of the Involute Curve According to Unit Darboux Vector With a New Method”. Turkish Journal of Science, vol. 5, no. 2, 2020, pp. 63-72.
Vancouver ŞENYURT S, ÇAKIR O. Calculation of the differential equations and harmonicity of the involute curve according to unit Darboux vector with a new method. TJOS. 2020;5(2):63-72.