Öz
Proje Numarası
FDK-2022-4238
Kaynakça
- 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
Öz
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.
Anahtar Kelimeler
Equivalent curve ruled surface developable surface equivalence class
Destekleyen Kurum
Çanakkale Onsekiz Mart University The Scientific Research Projects Coordination Unit
Proje Numarası
FDK-2022-4238
Kaynakça
- 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
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebirsel ve Diferansiyel Geometri |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Proje Numarası | FDK-2022-4238 |
| Erken Görünüm Tarihi | 20 Nisan 2025 |
| Yayımlanma Tarihi | 24 Nisan 2025 |
| Gönderilme Tarihi | 6 Ağustos 2024 |
| Kabul Tarihi | 1 Kasım 2024 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 18 Sayı: 1 |
