Research Article
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Year 2025, , 135 - 142, 24.04.2025

Büşra Bataray , Çetin Camcı

https://doi.org/10.36890/iejg.1528951

Abstract

Project Number

FDK-2022-4238

References

  • Camcı, Ç., Uçum, A., ˙Ilarslan, K.: Space curves related by a transformation of Combescure. Journal of Dynamical Systems and GeometricTheories. 19 (2), 271-287 (2021). https://doi.org/10.1080/1726037X.2021.2011113
  • Catalan, E.: Sur les surface réglées dont l’aire est un minimum. Journal de mathématiques pures et appliquées. 7 (1), 203-211 (1842).
  • Dalkıran, G.: A new approach to generation of ruled surfaces. MSc thesis. Eski¸sehir Osmangazi University (2008).
  • Do Carmo, M. P.: Differential geometry of curves and surfaces. Prentice-Hall, Inc., Englewood Cliffs. New Jersey (1976).
  • Graustein, W. C.: On two related transformations of space curves. American Journal of Mathematics. 39 (3), 233-240 (1917).
  • Hathout, F., Bekar, M., Yaylı, Y.: Ruled surfaces and tangent bundle of unit 2-sphere. International Journal of Geometric Methods in Modern Physics. 14 (10), 1750145 (2017). https://doi.org/10.1142/S0219887817501456
  • Izumiya, S., Takeuchi, N.: Special curves and ruled curves. Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry. 44 (1), 203-212 (2003).
  • Izumiya, S., Takeuchi, N.: New special curves and developable surfaces. Turkish Journal of Mathematics. 28 (2), 153-163 (2004).
  • Karaca, E.: Some characterizations for curves and surfaces in dual space. Ph.D. thesis. Gazi University (2020).
  • Karakaş, B., Gündo˘gan, H.: A relation among DS 2, TS 2 and non-cylindrical ruled surfaces. Mathematical Communications. 8 (1), 9-14, (2003).
  • Monge, G.: Géométrie Descriptive. Paris (1795).
  • Önder, M.: Slant ruled surfaces. Preprint arxiv:1311.0627 (2013).
  • Önder, M., Kaya, O.: Darboux slant ruled surfaces. Azerbaijan Journal of Mathematics. 5 (1), 64-72 (2015).
  • Önder, M., Kahraman, T.: On rectifying ruled surfaces. Kuwait Journal of Science. 47 (4), 1-11 (2020).
  • Sannia, G.: Trasformazione de Combescure ed altre analoghe per le curve storte. Rendiconti del Circolo Matematico di Palermo. 20 (1), 83-92 (1905).
  • Study, E.: Geometrie Der Dynamen. Leipzig (1903).
  • Subba Rao, H. S.: A note on space curves. Mathematics Magazine. 33 (3), 162-164 (1960). https://doi.org/10.2307/3029038

Applications of Equivalent Curves to Ruled Surfaces

Year 2025, , 135 - 142, 24.04.2025

Büşra Bataray , Çetin Camcı

https://doi.org/10.36890/iejg.1528951

Abstract

In this paper, the characterization of equivalent curves in E^3 is used to define ruled surfaces whose base curves are equivalent curves and to examine the relationships between them. At the same time, an equivalence relation for ruled surfaces is obtained. The equivalence classes resulting from this relation are studied. It is concluded that all ruled surfaces in the equivalence class of a developable surface are developable. Thus, a method is established to obtain an infinite ruled surface from a ruled surface. Finally, a new method is given to obtain a developable surface.

Keywords

Equivalent curve ruled surface developable surface equivalence class

Supporting Institution

Çanakkale Onsekiz Mart University The Scientific Research Projects Coordination Unit

Project Number

FDK-2022-4238

References

  • Camcı, Ç., Uçum, A., ˙Ilarslan, K.: Space curves related by a transformation of Combescure. Journal of Dynamical Systems and GeometricTheories. 19 (2), 271-287 (2021). https://doi.org/10.1080/1726037X.2021.2011113
  • Catalan, E.: Sur les surface réglées dont l’aire est un minimum. Journal de mathématiques pures et appliquées. 7 (1), 203-211 (1842).
  • Dalkıran, G.: A new approach to generation of ruled surfaces. MSc thesis. Eski¸sehir Osmangazi University (2008).
  • Do Carmo, M. P.: Differential geometry of curves and surfaces. Prentice-Hall, Inc., Englewood Cliffs. New Jersey (1976).
  • Graustein, W. C.: On two related transformations of space curves. American Journal of Mathematics. 39 (3), 233-240 (1917).
  • Hathout, F., Bekar, M., Yaylı, Y.: Ruled surfaces and tangent bundle of unit 2-sphere. International Journal of Geometric Methods in Modern Physics. 14 (10), 1750145 (2017). https://doi.org/10.1142/S0219887817501456
  • Izumiya, S., Takeuchi, N.: Special curves and ruled curves. Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry. 44 (1), 203-212 (2003).
  • Izumiya, S., Takeuchi, N.: New special curves and developable surfaces. Turkish Journal of Mathematics. 28 (2), 153-163 (2004).
  • Karaca, E.: Some characterizations for curves and surfaces in dual space. Ph.D. thesis. Gazi University (2020).
  • Karakaş, B., Gündo˘gan, H.: A relation among DS 2, TS 2 and non-cylindrical ruled surfaces. Mathematical Communications. 8 (1), 9-14, (2003).
  • Monge, G.: Géométrie Descriptive. Paris (1795).
  • Önder, M.: Slant ruled surfaces. Preprint arxiv:1311.0627 (2013).
  • Önder, M., Kaya, O.: Darboux slant ruled surfaces. Azerbaijan Journal of Mathematics. 5 (1), 64-72 (2015).
  • Önder, M., Kahraman, T.: On rectifying ruled surfaces. Kuwait Journal of Science. 47 (4), 1-11 (2020).
  • Sannia, G.: Trasformazione de Combescure ed altre analoghe per le curve storte. Rendiconti del Circolo Matematico di Palermo. 20 (1), 83-92 (1905).
  • Study, E.: Geometrie Der Dynamen. Leipzig (1903).
  • Subba Rao, H. S.: A note on space curves. Mathematics Magazine. 33 (3), 162-164 (1960). https://doi.org/10.2307/3029038
There are 17 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Büşra Bataray 0000-0001-7828-4283

Çetin Camcı 0000-0002-0122-559X

Project Number FDK-2022-4238
Early Pub Date April 20, 2025
Publication Date April 24, 2025
Submission Date August 6, 2024
Acceptance Date November 1, 2024
Published in Issue Year 2025

Cite

APA Bataray, B., & Camcı, Ç. (2025). Applications of Equivalent Curves to Ruled Surfaces. International Electronic Journal of Geometry, 18(1), 135-142. https://doi.org/10.36890/iejg.1528951
AMA Bataray B, Camcı Ç. Applications of Equivalent Curves to Ruled Surfaces. Int. Electron. J. Geom. April 2025;18(1):135-142. doi:10.36890/iejg.1528951
Chicago Bataray, Büşra, and Çetin Camcı. “Applications of Equivalent Curves to Ruled Surfaces”. International Electronic Journal of Geometry 18, no. 1 (April 2025): 135-42. https://doi.org/10.36890/iejg.1528951.
EndNote Bataray B, Camcı Ç (April 1, 2025) Applications of Equivalent Curves to Ruled Surfaces. International Electronic Journal of Geometry 18 1 135–142.
IEEE B. Bataray and Ç. Camcı, “Applications of Equivalent Curves to Ruled Surfaces”, Int. Electron. J. Geom., vol. 18, no. 1, pp. 135–142, 2025, doi: 10.36890/iejg.1528951.
ISNAD Bataray, Büşra - Camcı, Çetin. “Applications of Equivalent Curves to Ruled Surfaces”. International Electronic Journal of Geometry 18/1 (April 2025), 135-142. https://doi.org/10.36890/iejg.1528951.
JAMA Bataray B, Camcı Ç. Applications of Equivalent Curves to Ruled Surfaces. Int. Electron. J. Geom. 2025;18:135–142.
MLA Bataray, Büşra and Çetin Camcı. “Applications of Equivalent Curves to Ruled Surfaces”. International Electronic Journal of Geometry, vol. 18, no. 1, 2025, pp. 135-42, doi:10.36890/iejg.1528951.
Vancouver Bataray B, Camcı Ç. Applications of Equivalent Curves to Ruled Surfaces. Int. Electron. J. Geom. 2025;18(1):135-42.