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Year 2021, Volume: 4 Issue: 2, 109 - 117, 31.07.2021

Fatma Ates

https://doi.org/10.33773/jum.952868

Abstract

References

  • A.T. Ali, H.S. Aziz, A.H. Sorour, Ruled Surfaces Generated by Some Special Curves in Euclidean 3-space, Journal of the Egyp. Math. Soc., 21, pp.285-294 (2013).
  • A.T. Ali, Position Vectors of Curves in the Galilean Space G3 Matematiqki Vesnik, 64(3), pp.200-210 (2012).
  • M.E. Aydın, M.A. Kulahci, A.O. Ogrenmis, Constant curvature translation surfaces in Galilean 3-space. International Electronic Journal of Geometry. 12(1), pp.9-19 (2019).
  • B. Divjak and Z. Milin-Sipus, Special curves on ruled surfaces in Galilean and pseudo-Galilean space, Acta Math. Hungar. 98, pp.175-187, (2003).
  • M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18, pp.209-217, (2013).
  • M. Dede, Tube surfaces in pseudo-Galilean space, Int. J. Geom. Methods Mod. Phys., 13, pp.10-16 (2016).
  • M. Dede, C. Ekici, W. Goemans, Y. Unluturk, Twisted surfaces with vanishing curvature in Galilean 3-space, Int. J. Geom. Methods Mod. Phys., 15(1), 1850001, 13pp. (2018).
  • M. Dede, C. Ekici, W. Goemans, Surfaces of revolution with vanishing curvature in Galilean 3-space, J. Math. Phys. Anal. Geom. 14, no. 2, pp.141-152, (2018).
  • F. Dillen and W. Sodsiri, Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom. 83, pp.10-21, (2005).
  • O. Gursoy, On the integral invariants of a closed ruled surface, J. Geom. 39, pp.80-91, (1990).
  • Z.M. Sipus and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Sci., 12, pp.1-28, (2012).
  • B.J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space G3, Glasnik Matematicki, 22(42), pp.449-457, (1987).
  • A. Turgut and H.H. Hacisalihoglu, Spacelike ruled surfaces in the Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Ser. Math. Stat., 46, pp.83-91, (1997).
  • C.E. Weatherburn, Differential geometry of three dimensions, Syndic of Cambridge University press, (1981).

RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE

Year 2021, Volume: 4 Issue: 2, 109 - 117, 31.07.2021

Fatma Ates

https://doi.org/10.33773/jum.952868

Abstract

The object of this paper is to investigate the properties of the ruled surface which direction vector has a constant slope with osculator plane of the base curve in Galiean $3-$space. We obtain some properties of this kind of ruled surface by calculating the geometric invariants. Also, we give an application on the example and their graphs are visualized by using the Mathematica program.

Keywords

Ruled surface Constant slope surface Striction curve Developable surface Minimal surface.

References

  • A.T. Ali, H.S. Aziz, A.H. Sorour, Ruled Surfaces Generated by Some Special Curves in Euclidean 3-space, Journal of the Egyp. Math. Soc., 21, pp.285-294 (2013).
  • A.T. Ali, Position Vectors of Curves in the Galilean Space G3 Matematiqki Vesnik, 64(3), pp.200-210 (2012).
  • M.E. Aydın, M.A. Kulahci, A.O. Ogrenmis, Constant curvature translation surfaces in Galilean 3-space. International Electronic Journal of Geometry. 12(1), pp.9-19 (2019).
  • B. Divjak and Z. Milin-Sipus, Special curves on ruled surfaces in Galilean and pseudo-Galilean space, Acta Math. Hungar. 98, pp.175-187, (2003).
  • M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18, pp.209-217, (2013).
  • M. Dede, Tube surfaces in pseudo-Galilean space, Int. J. Geom. Methods Mod. Phys., 13, pp.10-16 (2016).
  • M. Dede, C. Ekici, W. Goemans, Y. Unluturk, Twisted surfaces with vanishing curvature in Galilean 3-space, Int. J. Geom. Methods Mod. Phys., 15(1), 1850001, 13pp. (2018).
  • M. Dede, C. Ekici, W. Goemans, Surfaces of revolution with vanishing curvature in Galilean 3-space, J. Math. Phys. Anal. Geom. 14, no. 2, pp.141-152, (2018).
  • F. Dillen and W. Sodsiri, Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom. 83, pp.10-21, (2005).
  • O. Gursoy, On the integral invariants of a closed ruled surface, J. Geom. 39, pp.80-91, (1990).
  • Z.M. Sipus and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Sci., 12, pp.1-28, (2012).
  • B.J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space G3, Glasnik Matematicki, 22(42), pp.449-457, (1987).
  • A. Turgut and H.H. Hacisalihoglu, Spacelike ruled surfaces in the Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Ser. Math. Stat., 46, pp.83-91, (1997).
  • C.E. Weatherburn, Differential geometry of three dimensions, Syndic of Cambridge University press, (1981).
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Fatma Ates 0000-0002-3529-1077

Publication Date July 31, 2021
Submission Date June 15, 2021
Acceptance Date July 26, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Ates, F. (2021). RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE. Journal of Universal Mathematics, 4(2), 109-117. https://doi.org/10.33773/jum.952868
AMA Ates F. RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE. JUM. July 2021;4(2):109-117. doi:10.33773/jum.952868
Chicago Ates, Fatma. “RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE”. Journal of Universal Mathematics 4, no. 2 (July 2021): 109-17. https://doi.org/10.33773/jum.952868.
EndNote Ates F (July 1, 2021) RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE. Journal of Universal Mathematics 4 2 109–117.
IEEE F. Ates, “RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE”, JUM, vol. 4, no. 2, pp. 109–117, 2021, doi: 10.33773/jum.952868.
ISNAD Ates, Fatma. “RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE”. Journal of Universal Mathematics 4/2 (July 2021), 109-117. https://doi.org/10.33773/jum.952868.
JAMA Ates F. RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE. JUM. 2021;4:109–117.
MLA Ates, Fatma. “RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE”. Journal of Universal Mathematics, vol. 4, no. 2, 2021, pp. 109-17, doi:10.33773/jum.952868.
Vancouver Ates F. RULED SURFACE WITH CONSTANT SLOPE ACCORDING TO OSCULATING PLANE OF BASE CURVE IN GALILEAN 3- SPACE. JUM. 2021;4(2):109-17.
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