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On Evolution of Some Associated Type Ruled Surfaces

Year 2020, , 178 - 186, 15.10.2020
https://doi.org/10.36753/mathenot.750639

Abstract

In this study, we define three new type ruled surfaces obtained by using the evolution of involute-evolute curve pair in Euclidean 3-space. Then, we give some nice results for the Gaussian curvature and the mean curvature of these surfaces. Moreover, considering the given involute-evolute curve pair, the graphics of these new type surfaces were drawn with the help of Mathematica.

References

  • Hacisalihoglu, H. H.: Differential geometry. Ankara University Faculty of Science Press. Ankara (2000).
  • Kuhnel, W.: Differential geometry: curves-surfaces-manifolds. Braunschweig. Wiesbaden (1999).
  • Sabuncuoglu, A.: Differential geometry. Nobel Press. Ankara (2014).
  • Ergut, M.: The drall and the scalar normal curvatures of (r+1)-dimensional generalized ruled surfaces. Commun. Fac.Sci. Univ. Ank. 38, 115-125 (1989).
  • Yılmaz, M.Y., Bektas, M., Ergut, M.: The pair of involute-evolute curves in Firsler manifold F3. Pure and Appl. Maths J. of Inst. of Kyrgyzstan National Academy, No. 39, Bishkek, (2008), 156-163.
  • Isah, MA., Kulahci, M.A.: Involute Curves in 4-Dimensional Galilean Space G4. Conference Proceedings of Science and Technology, 2(2), (2019), 134–141.
  • Do Carmo, M.: Differential geometry of curves and surfaces. Prentice-Hall. Englewood Cliffs (1976).
  • Gray, A.: Modern differential geometry of curves and surfaces with mathematica. CRC. New York (1998).
  • Nakayama, K., Wadati, M.: Motion of curves in the plane. J Phys. Soc. Japan.62, 473-479 (1993).
  • [Abdel-All, N. H., Hussien, R. A., Youssef, T.: Evolution of curves via the velocities of the moving frame. J. Math. Comput. Sci. 2, 1170-1185 (2012).
  • Doliwa, A., Santini, P.: An elementary geometric characterization of the integrable motions of a curve. Physics Letters A. 185, 373-384 (1994).
  • Kwon, D. Y., Park, F. C.: Evolution of inelastic plane curves. Applied Mathematics Letters.12, 115-119 (1999).
  • Rogers, C., Schief, W. K.: Bäcklund and Darboux transformations: Geometry and modern applications in soliton theory. Cambridge University Press (2002).
  • Abd-Ellah, H. N.: Evolution of translation surfaces in Euclidean 3-space. Applied Mathematics & Information Sciences. 9, 661-668 (2015).
  • Hussien, R. A., Mohamed, S. G.: Generated surfaces via inextensible flows of curves in R3. Journal of Applied Mathematics. Article ID: 6178961 (2016).
  • Kwon, D. Y., Park, F. C.: Inextensible flows of curves and developable surfaces. Applied Mathematics Letters.18,1156-1162 (2005).
  • Yildiz, O. G., Ersoy, S., Masal, M.: Note on inextensible flows of curves on oriented surface. CUBO A Mathematical Journal. 16(3), 11-19 (2014).
  • Nakayama, K., Wadati, M.: The motion of surfaces. J. Phys. Soc. of Japan.62, 1895-1901 (1993).
  • Hussien, R. A., Youssef, T.: Evolution of special ruled surfaces via the evolution of their directrices in Euclidean 3-space E3. Applied Mathematics & Information Sciences. 10, 1949-1956 (2016).
  • Soliman, M. A., Abdel-All, N. H., Hussien, R. A., Youssef, T.: Evolutions of the ruled surfaces via the evolution of their directrix using quasi frame along a space curve. Journal of Applied Mathematics and Physics.6(8), 1748-1756(2018).
  • Eren, K., Koksal, H. H.:Evolution of space curves and the special ruled Surfaces with modified orthogonal frame. AIMS Mathematics. 5(3), 2027–2039 (2020).
  • As, E., Sarıoglugil, A.: On the Bishop curvatures of involute-evolute curve couple in E3. International Journal of Physical Sciences. 9 (7), 140–145 (2014).
  • Boyer, C.: A History of mathematics. New York:Wiley. p. 334 (1968).
  • Çalışkan, M., Bilici, M.: Some characterizations for the pair of involute-evolute curves in Euclidean space E3. Bulletin of Pure and Applied Sciences. 2 E(2), 289-294 (2002).
  • Akyigit, M., Azak, A.Z., Ersoy, S.: Involute-evolute curves in Galilean space G3. Scientia Magna. 6(4), 75-80 (2010).
  • Bükcü, B., Karacan, M. K.: On the involute and evolute curves of the spacelike curve with a spacelike binormal inMinkowski 3-space. International Journal of Contemporary Mathematical Sciences.5(2), 221-232 (2007).
  • Senyurt, S., Altun, Y., Cevahir, C.: On the Darboux vector belonging to involute curve a different view. Mathematical Sciences and Applications E-Notes.4(2), 131-138 (2016).
  • [28] Yoon, DW., Yuzbasi, ZK., Aslan, EC.: Evolution of Spacelike Curves and Special Timelike Ruled Surfaces in the Minkowski Space. Preprint arXiv:1908.00053 (2019).
  • [29] Yuzbasi, ZK., Aslan, EC., Inc, M., Baleanu, D.: On exact solutions for new coupled nonlinear models getting evolution of curves in Galilean space. Thermal Science 23 (Suppl. 1), 227-233 (2019).
Year 2020, , 178 - 186, 15.10.2020
https://doi.org/10.36753/mathenot.750639

Abstract

References

  • Hacisalihoglu, H. H.: Differential geometry. Ankara University Faculty of Science Press. Ankara (2000).
  • Kuhnel, W.: Differential geometry: curves-surfaces-manifolds. Braunschweig. Wiesbaden (1999).
  • Sabuncuoglu, A.: Differential geometry. Nobel Press. Ankara (2014).
  • Ergut, M.: The drall and the scalar normal curvatures of (r+1)-dimensional generalized ruled surfaces. Commun. Fac.Sci. Univ. Ank. 38, 115-125 (1989).
  • Yılmaz, M.Y., Bektas, M., Ergut, M.: The pair of involute-evolute curves in Firsler manifold F3. Pure and Appl. Maths J. of Inst. of Kyrgyzstan National Academy, No. 39, Bishkek, (2008), 156-163.
  • Isah, MA., Kulahci, M.A.: Involute Curves in 4-Dimensional Galilean Space G4. Conference Proceedings of Science and Technology, 2(2), (2019), 134–141.
  • Do Carmo, M.: Differential geometry of curves and surfaces. Prentice-Hall. Englewood Cliffs (1976).
  • Gray, A.: Modern differential geometry of curves and surfaces with mathematica. CRC. New York (1998).
  • Nakayama, K., Wadati, M.: Motion of curves in the plane. J Phys. Soc. Japan.62, 473-479 (1993).
  • [Abdel-All, N. H., Hussien, R. A., Youssef, T.: Evolution of curves via the velocities of the moving frame. J. Math. Comput. Sci. 2, 1170-1185 (2012).
  • Doliwa, A., Santini, P.: An elementary geometric characterization of the integrable motions of a curve. Physics Letters A. 185, 373-384 (1994).
  • Kwon, D. Y., Park, F. C.: Evolution of inelastic plane curves. Applied Mathematics Letters.12, 115-119 (1999).
  • Rogers, C., Schief, W. K.: Bäcklund and Darboux transformations: Geometry and modern applications in soliton theory. Cambridge University Press (2002).
  • Abd-Ellah, H. N.: Evolution of translation surfaces in Euclidean 3-space. Applied Mathematics & Information Sciences. 9, 661-668 (2015).
  • Hussien, R. A., Mohamed, S. G.: Generated surfaces via inextensible flows of curves in R3. Journal of Applied Mathematics. Article ID: 6178961 (2016).
  • Kwon, D. Y., Park, F. C.: Inextensible flows of curves and developable surfaces. Applied Mathematics Letters.18,1156-1162 (2005).
  • Yildiz, O. G., Ersoy, S., Masal, M.: Note on inextensible flows of curves on oriented surface. CUBO A Mathematical Journal. 16(3), 11-19 (2014).
  • Nakayama, K., Wadati, M.: The motion of surfaces. J. Phys. Soc. of Japan.62, 1895-1901 (1993).
  • Hussien, R. A., Youssef, T.: Evolution of special ruled surfaces via the evolution of their directrices in Euclidean 3-space E3. Applied Mathematics & Information Sciences. 10, 1949-1956 (2016).
  • Soliman, M. A., Abdel-All, N. H., Hussien, R. A., Youssef, T.: Evolutions of the ruled surfaces via the evolution of their directrix using quasi frame along a space curve. Journal of Applied Mathematics and Physics.6(8), 1748-1756(2018).
  • Eren, K., Koksal, H. H.:Evolution of space curves and the special ruled Surfaces with modified orthogonal frame. AIMS Mathematics. 5(3), 2027–2039 (2020).
  • As, E., Sarıoglugil, A.: On the Bishop curvatures of involute-evolute curve couple in E3. International Journal of Physical Sciences. 9 (7), 140–145 (2014).
  • Boyer, C.: A History of mathematics. New York:Wiley. p. 334 (1968).
  • Çalışkan, M., Bilici, M.: Some characterizations for the pair of involute-evolute curves in Euclidean space E3. Bulletin of Pure and Applied Sciences. 2 E(2), 289-294 (2002).
  • Akyigit, M., Azak, A.Z., Ersoy, S.: Involute-evolute curves in Galilean space G3. Scientia Magna. 6(4), 75-80 (2010).
  • Bükcü, B., Karacan, M. K.: On the involute and evolute curves of the spacelike curve with a spacelike binormal inMinkowski 3-space. International Journal of Contemporary Mathematical Sciences.5(2), 221-232 (2007).
  • Senyurt, S., Altun, Y., Cevahir, C.: On the Darboux vector belonging to involute curve a different view. Mathematical Sciences and Applications E-Notes.4(2), 131-138 (2016).
  • [28] Yoon, DW., Yuzbasi, ZK., Aslan, EC.: Evolution of Spacelike Curves and Special Timelike Ruled Surfaces in the Minkowski Space. Preprint arXiv:1908.00053 (2019).
  • [29] Yuzbasi, ZK., Aslan, EC., Inc, M., Baleanu, D.: On exact solutions for new coupled nonlinear models getting evolution of curves in Galilean space. Thermal Science 23 (Suppl. 1), 227-233 (2019).
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Alev Kelleci 0000-0003-2528-2131

Kemal Eren 0000-0001-5273-7897

Publication Date October 15, 2020
Submission Date June 10, 2020
Acceptance Date October 27, 2020
Published in Issue Year 2020

Cite

APA Kelleci, A., & Eren, K. (2020). On Evolution of Some Associated Type Ruled Surfaces. Mathematical Sciences and Applications E-Notes, 8(2), 178-186. https://doi.org/10.36753/mathenot.750639
AMA Kelleci A, Eren K. On Evolution of Some Associated Type Ruled Surfaces. Math. Sci. Appl. E-Notes. October 2020;8(2):178-186. doi:10.36753/mathenot.750639
Chicago Kelleci, Alev, and Kemal Eren. “On Evolution of Some Associated Type Ruled Surfaces”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 178-86. https://doi.org/10.36753/mathenot.750639.
EndNote Kelleci A, Eren K (October 1, 2020) On Evolution of Some Associated Type Ruled Surfaces. Mathematical Sciences and Applications E-Notes 8 2 178–186.
IEEE A. Kelleci and K. Eren, “On Evolution of Some Associated Type Ruled Surfaces”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 178–186, 2020, doi: 10.36753/mathenot.750639.
ISNAD Kelleci, Alev - Eren, Kemal. “On Evolution of Some Associated Type Ruled Surfaces”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 178-186. https://doi.org/10.36753/mathenot.750639.
JAMA Kelleci A, Eren K. On Evolution of Some Associated Type Ruled Surfaces. Math. Sci. Appl. E-Notes. 2020;8:178–186.
MLA Kelleci, Alev and Kemal Eren. “On Evolution of Some Associated Type Ruled Surfaces”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 178-86, doi:10.36753/mathenot.750639.
Vancouver Kelleci A, Eren K. On Evolution of Some Associated Type Ruled Surfaces. Math. Sci. Appl. E-Notes. 2020;8(2):178-86.

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