On parallel p-equidistant ruled surfaces by using mofied orthogonal frame with curvature in E³
DOI:
https://doi.org/10.5269/bspm.40601Abstract
In this paper, it is investigated Ruled surfaces according to modified orthogonal frame with curvature in 3-dimensional Euclidean space. Firstly, we give apex angle, pitch and drall of closed ruled surface in E³. Then, it characterized the relationship between these invariant of parallel p-equidistant ruled surfaces.
References
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24. B. O'Neil, Elementary Differential Geometry, Academic Press, New York, 1967.
25. M. Onder, H. H. Ugurlu, Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Space, arXiv:1007.2041v2 [math.DG], arXiv:1005.2570v3 [math.DG].
26. D. Unal, I. Kisi, M. Tosun, Spinor Bishop Equations of Curves in Euclidean 3-Space, Adv. Appl. Clifford Algebras, 23 (2013), 757-765. https://doi.org/10.1007/s00006-013-0390-8
27. S. Yılmaz, M. Turgut, A New Version of Bishop Frame and an Application to Spherical Images, J. Math. Anal. and Ap., 2 (371) (2010), 764-776. https://doi.org/10.1016/j.jmaa.2010.06.012
2. V. Asil, S. Bas, T. Korpinar, On construction of D-focal curves in Euclidean 3-space M3, Bol. Soc. Paran. Mat., 31 (2) (2013), 273-277. https://doi.org/10.5269/bspm.v31i2.18616
3. L. R. Bishop, There is More Than One Way to Frame a Curve, Amer. Math. Monthly, 82 (3) (1975), 246-251. https://doi.org/10.1080/00029890.1975.11993807
4. J. E. Brosius, Rank 2-Vector Bundles on a Ruled Surface, Math. Ann., 256 (1983), 155-168. https://doi.org/10.1007/BF01460796
5. B. Bukcu, M. K. Karacan, On The Modified Orthogonal Frame with Curvature and Torsion in 3-Space, Mathematıcal Scıences And Applıcatıons E-Notes, 4(1) (2016), 184-188. https://doi.org/10.36753/mathenot.421429
6. B. Bukcu, M. K. Karacan, Spherical Curves with Modified Orthogonal Frame, J. New Res. Sci., 10 (2016), 60-68.
7. H. H. Hacısalioglu, Diferansiyel Geometri, Ankara Universitesi Fen Fakultesi, 1994.
8. T. Korpınar, M. T. Sarıaydın, Essin Turhan, Associated Curves According to Bishop Fr ame in Euclidean 3-Space, Adv. Model. Opt., 3 (15) (2013), 713-717.
9. T. Korpınar, V. Asil, M. T. Sarıaydın and M. Incesu, A Characterization for Bishop Equations of Parallel Curves According to Bishop Frame in E3, Bol. Soc. Paran. Mat, 33 (1) (2015), 33-39. https://doi.org/10.5269/bspm.v33i1.21712
10. T. Korpınar, S. Ba¸s, On evolute curves in terms of inextensible flows of in E3, Bol. Soc. Paran. Mat., 36 (1) (2018), 117-124. https://doi.org/10.5269/bspm.v36i1.31619
11. T. Korpinar, E. Turhan, Tubular Surfaces Around Timelike Biharmonic Curves in Lorentzian Heisenberg Group Heis3, An. St. Univ., Ovidus Constanta, 1 (20) (2012), 431-446. https://doi.org/10.2478/v10309-012-0029-0
12. T. Korpinar, E. Turhan, Time-Tangent Surfaces Around Biharmonic Particles and Its Lorentz Transformations in Heisenberg Space-Time, Int. J. Theor. Phys., 52 (2013), 4427-4438. https://doi.org/10.1007/s10773-013-1761-6
13. T. Korpınar, E. Turhan, On characterization of B-canal surfaces in terms of biharmonic B-slant helices according to Bishop frame in Heisenberg group Heis3, J. Math. Anal. Appl. 382 (2011), 57-65. https://doi.org/10.1016/j.jmaa.2011.04.029
14. T. Korpınar, B-tubular surfaces in Lorentzian Heisenberg Group H3, Acta Scientiarum. Technology 37(1) (2015), 63-69 https://doi.org/10.4025/actascitechnol.v37i1.16670
15. T. Korpınar, E. Turhan, A New Version of Time-Pencil Surfaces Around Biharmonic Particles and Its Lorentz Transformations in Heisenberg Spacetime. Int. J. Theor. Phys. 53 (2014), 2288-2302 https://doi.org/10.1007/s10773-014-2029-5
16. T. Korpınar, E. Turhan, Time-Canal Surfaces Around Biharmonic Particles and Its Lorentz Transformations in Heisenberg Spacetime. Int. J. Theor. Phys. 53 (2014), 1502-1520 https://doi.org/10.1007/s10773-013-1950-3
17. T. Korpınar, B-tubular surfaces in Lorentzian Heisenberg Group H3, Acta Scientiarum. Technology 37(1) (2015), 63-69 https://doi.org/10.4025/actascitechnol.v37i1.16670
18. T. Korpınar, New characterization of b-m2 developable surfaces, Acta Scientiarum. Technology 37(2) (2015), 245-250 https://doi.org/10.4025/actascitechnol.v37i2.17368
19. Z. S. Korpinar, M. Tuz, T. Korpinar, New Electromagnetic Fluids Inextensible Flows of Spacelike Particles and some Wave Solutions in Minkowski Space-time, Int J Theor Phys 55 (1) (2016), 8-16. https://doi.org/10.1007/s10773-015-2629-8
20. W. Kuhnel, Curves- Surfaces- Manifolds, Differantial Geometry, Amer. Math. Soc., 2003.
21. M. Masal, N.Kuruoglu, Spacelike Parallel p-Equidistant Ruled Surfaces in the Minkowski 3-Space, Algebra Group and Geometry, 22 (2005),13-24.
22. M. Masal, (m+1)-Dimensional Spacelike Parallel pi-Equidistant Ruled Surfaces in the Minkowski Space Rn 1, Novi Sad J. Math., 1 (36) (2006), 55-63.
23. K. Orbay, E. Kasap, I. Aydemir, Mannheim offsets of ruled surfaces, Mathematical Problems in Engineering, (2009), Article ID 160917. https://doi.org/10.1155/2009/160917
24. B. O'Neil, Elementary Differential Geometry, Academic Press, New York, 1967.
25. M. Onder, H. H. Ugurlu, Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Space, arXiv:1007.2041v2 [math.DG], arXiv:1005.2570v3 [math.DG].
26. D. Unal, I. Kisi, M. Tosun, Spinor Bishop Equations of Curves in Euclidean 3-Space, Adv. Appl. Clifford Algebras, 23 (2013), 757-765. https://doi.org/10.1007/s00006-013-0390-8
27. S. Yılmaz, M. Turgut, A New Version of Bishop Frame and an Application to Spherical Images, J. Math. Anal. and Ap., 2 (371) (2010), 764-776. https://doi.org/10.1016/j.jmaa.2010.06.012
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2021-12-16
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