Abstract
In this study, we have given the necessary and sufficient conditions for a Mannheim D pair curve to be both isoparametric and asymptotic on a surface. By using this, we have formed the parametrization for the family of surfaces accepting the basis curve as a Mannheim D- pair as an asymptotic curve. Moreover, we have extended the idea to the ruled surfaces and examined the conditions for those to be developable. Finally, we have presented some examples to illustrate the surfaces with a common Mannheim D- asymptotic curve.
References
- Referans1 Atalay G Ş (2018). Surfaces Family with a Common Mannheim Asymptotic Curve. Journal of Applied Mathematics and Computation 2(4): 143-154
- Referans2 Bayram E, Güler F & Kasap E (2012). Parametric representation of a surface pencil with a common asymptotic curve. Computer-Aided Design 44(7): 637-643
- Referans3 Kazaz M, Ugurlu H H, Önder M & Kahraman T (2015). Mannheim partner D-curves in the Euclidean 3-space E3. New Trends in Mathematical Sciences 3(2): 24-35
- Referans4 Lee J W (2011). No Null-Helix Mannheim Curves in the Minkowski Space 𝔼𝟑𝟏. International Journal of Mathematics and Mathematical Sciences: 1-7
- Referans5 Liu H & Wang F (2008). Mannheim partner curves in 3-space. Journal of Geometry 88(1-2): 120-126
- Referans6 Mannheim A (1878). De l'emploi de la courbe représentative de la surface des normales principales d'une courbe gauche pour la démonstration de propriétés relatives à cette courbure. C.R. Comptes Rendus des Séances de l'Académie des Sciences. Paris. 86 1254-1256
- Referans7 7. O’Neill B (1966). Elementary Differential Geometry. Academic Press Inc., New York
Abstract
Bu çalışmada, herhangi bir Mannheim D- eğri çiftinin bir yüzey üzerinde hem izoparametrik hem de asimtotik olması için gerekli ve yeterli şartlar verildi. Bundan yola çıkarak dayanak eğrisini asimtotik Mannheim D- eğrisi kabul eden yüzeyler ailesinin parametrik formu oluşturuldu. İlgili fikir aynı zamanda regle yüzeylere de genişletilerek, bu regle yüzeyler için açılabilir olma şartları incelendi. Son olarak, ortak Mannheim D- isoasimtotik eğrili yüzey aileleri için bazı örnekler sunuldu.
References
- Referans1 Atalay G Ş (2018). Surfaces Family with a Common Mannheim Asymptotic Curve. Journal of Applied Mathematics and Computation 2(4): 143-154
- Referans2 Bayram E, Güler F & Kasap E (2012). Parametric representation of a surface pencil with a common asymptotic curve. Computer-Aided Design 44(7): 637-643
- Referans3 Kazaz M, Ugurlu H H, Önder M & Kahraman T (2015). Mannheim partner D-curves in the Euclidean 3-space E3. New Trends in Mathematical Sciences 3(2): 24-35
- Referans4 Lee J W (2011). No Null-Helix Mannheim Curves in the Minkowski Space 𝔼𝟑𝟏. International Journal of Mathematics and Mathematical Sciences: 1-7
- Referans5 Liu H & Wang F (2008). Mannheim partner curves in 3-space. Journal of Geometry 88(1-2): 120-126
- Referans6 Mannheim A (1878). De l'emploi de la courbe représentative de la surface des normales principales d'une courbe gauche pour la démonstration de propriétés relatives à cette courbure. C.R. Comptes Rendus des Séances de l'Académie des Sciences. Paris. 86 1254-1256
- Referans7 7. O’Neill B (1966). Elementary Differential Geometry. Academic Press Inc., New York
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 31, 2020 |
| Submission Date | November 20, 2020 |
| Published in Issue | Year 2020 Volume: 10 Issue: 2 |