On parallel p-equidistant ruled surfaces by using mofied orthogonal frame with curvature in E³
Resumo
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.
Downloads
Referências
E. As, S. Senyurt, Some Characteristic Properties of Parallel z-Equidistant Ruled Surfaces, Math. Prob. in Eng., https://doi.org/10.1155/2013/587289
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
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
J. E. Brosius, Rank 2-Vector Bundles on a Ruled Surface, Math. Ann., 256 (1983), 155-168. https://doi.org/10.1007/BF01460796
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
B. Bukcu, M. K. Karacan, Spherical Curves with Modified Orthogonal Frame, J. New Res. Sci., 10 (2016), 60-68.
H. H. Hacısalioglu, Diferansiyel Geometri, Ankara Universitesi Fen Fakultesi, 1994.
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.
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
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
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
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
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
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
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
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
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
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
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
W. Kuhnel, Curves- Surfaces- Manifolds, Differantial Geometry, Amer. Math. Soc., 2003.
M. Masal, N.Kuruoglu, Spacelike Parallel p-Equidistant Ruled Surfaces in the Minkowski 3-Space, Algebra Group and Geometry, 22 (2005),13-24.
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.
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
B. O'Neil, Elementary Differential Geometry, Academic Press, New York, 1967.
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].
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
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
Copyright (c) 2021 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
