Abstract
Bu çalışmada, verilen bir eğrinin Mannheim D- çiftini üzerinde jeodezik olarak kabul eden yüzeylerin parametrik formu inşa edildi. Yüzey, Darbaux çatısının lineer bir bileşimi olarak ifade edilerek, üzerinde bulundurduğu Mannheim D- eğri çiftinin izoparametrik ve jeodezik olması için gerekli ve yeterli şartlar tanımlandı. Mevcut tanımlamalar regle yüzeyler için ayrıca ele alındı. Son olaraksa ortak Mannheim D- izogeodezik eğrili yüzeylere bazı örnekler verildi.
References
- Referans1 Blum R (1966). A remarkable class of Mannheim-curves. Canadian Mathematical Bulletin 9: 223-228
- Referans2 Guan, Z., Ling, J., Tao, N., Ping, X., & Rongxi, T. (1997). Study and application of physics-based deformable curves and surfaces. Computers & Graphics 21(3): 305-313
- Referans3 Izumiya S & Takeuchi N (2003). Special Curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry 44(1): 203-212
- Referans4 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
- Referans5 Lee J W (2011). No Null-Helix Mannheim Curves in the Minkowski Space 𝔼𝟑𝟏. International Journal of Mathematics and Mathematical Sciences: 1-7
- Referans6 Liu H & Wang F (2008). Mannheim partner curves in 3-space. Journal of Geometry 88(1-2): 120-126
- Referans7 Lockwood E H (1967). A book of curves. Cambridge University Press
- Referans8 O'neill B (2014). Elementary differential geometry. Academic press
- Referans9 Petrovic, M., Verstraelen, J., & Verstraelen, L. (2000). Principal normal spectral variations of space curves. Proyecciones (Antofagasta), 19(2), 141-155
- Referans10 Wang G J, Tang K & Tai C L (2004). Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design, 36(5), 447-459
Abstract
In this paper, we construct the parameterization of surface family possessing a Mannheim D pair of a given curve as a geodesic. By using the Darboux frame, we present the surface as a linear combination of this frame and analyze the necessary and sufficient condition for a given curve such that its Mannheim D pair is both isoparametric and geodesic on a parametric surface. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces with common Mannheim D isogeodesic curve.
References
- Referans1 Blum R (1966). A remarkable class of Mannheim-curves. Canadian Mathematical Bulletin 9: 223-228
- Referans2 Guan, Z., Ling, J., Tao, N., Ping, X., & Rongxi, T. (1997). Study and application of physics-based deformable curves and surfaces. Computers & Graphics 21(3): 305-313
- Referans3 Izumiya S & Takeuchi N (2003). Special Curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry 44(1): 203-212
- Referans4 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
- Referans5 Lee J W (2011). No Null-Helix Mannheim Curves in the Minkowski Space 𝔼𝟑𝟏. International Journal of Mathematics and Mathematical Sciences: 1-7
- Referans6 Liu H & Wang F (2008). Mannheim partner curves in 3-space. Journal of Geometry 88(1-2): 120-126
- Referans7 Lockwood E H (1967). A book of curves. Cambridge University Press
- Referans8 O'neill B (2014). Elementary differential geometry. Academic press
- Referans9 Petrovic, M., Verstraelen, J., & Verstraelen, L. (2000). Principal normal spectral variations of space curves. Proyecciones (Antofagasta), 19(2), 141-155
- Referans10 Wang G J, Tang K & Tai C L (2004). Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design, 36(5), 447-459
Details
| Primary Language | English |
|---|---|
| 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 |