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On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$

Yıl 2023, Cilt: 72 Sayı: 4, 867 - 879, 29.12.2023

Semra Yurttançıkmaz

https://doi.org/10.31801/cfsuasmas.1187854

Öz

In this paper, it has been researched curves lying on parallel-like surfaces $M^{f}$ of the ruled surface $M$ in $E^{3}$. Using the definition of parallel-like surfaces it has been found parametric expressions of parallel-like surface of the ruled surface and image curve of the directrix curve of the base surface. Moreover, obtaining Darboux frames of curves lying on surfaces $M$ and $M^{f}$, it has been compared the geodesic curvatures, the normal curvatures and the geodesic torsions of these curves.

Anahtar Kelimeler

Ruled surface parallel-like surface Darboux frame

Kaynakça

  • Ali, A.T., Non-lightlike constant angle ruled surfaces in Minkowski 3-space, Journal of Geometry and Physics, 157 (2020), 1-10. https://doi.org/10.1016/j.geomphys.2020.103833
  • Gray, A., Abbena, E., Salamon, S., Modern Differential Geometry of Curves and Surfaces with Mathematica (Third Edition), Studies in Advanced Mathematics, 2006.
  • Güler, F., An approach for designing a developable and minimal ruled surfaces using the curvature theory, Int. J. Geom. Methods Mod. Phys., 18(1) (2021), 2150015. https://doi.org/10.1142/S0219887821500158
  • Hacısalihoğlu, H.H., Differential Geometry, İnönü University Faculty of Arts and Sciences Publications, Ankara, 1983.
  • Hagen, H., Pottmann, H., Divivier, A., Visualization functions on a surface, Journal of Visualization and Animation, 2 (1991), 52-58. https://doi.org/10.1002/vis.4340020205
  • Hagen, H., Stefanie, H., Schreiber, T., Visualization and computation of curvature behaviour of freeform curves and surfaces, Comput.-Aided Des., 27 (1995), 545-552. https://doi.org/10.1016/0010-4485(95)93587-P
  • Hashemian, A., Bo, P., Barton, M., Reparameterization of ruled surfaces: toward generating smooth jerk-minimized toolpaths for multi-axis flank CNC milling, Comput.-Aided Des., 127 (2020), 102868. https://doi.org/10.1016/j.cad.2020.102868
  • Körpınar, T., Ünlütürk, Y., A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space, Int. J. Nonlinear Sci. Numer. Simul., 22(7-8) (2021), 917-926. https://doi.org/10.1515/ijnsns-2019-0306
  • Kuhnel, W., Differential Geometry Curves-Surfaces-Manifolds, Wiesbaden Braunchweig, 1999.
  • Lee, W., Park, E., On curves lying on a rational normal surface scroll, J. Pure Appl. Algebra, 223(10) (2019), 4458-4476. https://doi.org/10.1016/j.jpaa.2019.01.016
  • Sabuncuoğlu, A., Differential Geometry, Nobel Publications, 2006.
  • Sağlam, D., Kalkan, Ö., Surfaces at a constant distance from the edge of regression on a surface in $E^{3}_{1}$ , Differential Geometry-Dynamical Systems, 12 (2010), 187-200.
  • Kızıltuğ, S., Tarakcı, Ö., Yaylı, Y., On the curves lying on parallel surfaces in the Euclidean 3-space $E^{3}$, Journal of Advanced Research in Dynamical and Control Systems, 5 (2013), 26-35.
  • Kızıltuğ, S., Yaylı, Y., Timelike curves on timelike parallel surfaces in Minkowski 3-space $E^{3}_{1}$ , Math. Æterna, 2 (2012), 689-700.
  • Sun, S., Yan, S., Jiang, S., Sun, Y., A high-accuracy tool path generation (HATPG) method for 5-axis flank milling of ruled surfaces with a conical cutter based on instantaneous envelope surface modelling, Comput.-Aided Des., 151 (2022), 103354. https://doi.org/10.1016/j.cad.2022.103354
  • Tarakcı, Ö., Hacısalihoğlu, H.H., Surfaces at a constant distance from the edge of regression on a surface, Applied Mathematics and Computation, 155 (2004), 81-93. https://doi.org/10.1016/S0096-3003(03)00761-6
  • Tarakcı, Ö., Surfaces at a Constant Distance from the Edge of Regression on a Surface, PhD thesis, Ankara University Institute of Science, 2002.
  • Yurttançıkmaz, S., Tarakcı, Ö., The relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface, Adv. Math. Phys., 2015 (2015), Article ID 397126, 1-6. https://doi.org/10.1155/2015/397126
  • Yurttançıkmaz, S., Tarakcı, Ö., Image curves on the parallel-like surfaces in $E^{3}$, Int. Electron. J. Geom., 16(1) (2023), 122-131. doi:10.36890/iejg.1178434

Yıl 2023, Cilt: 72 Sayı: 4, 867 - 879, 29.12.2023

Semra Yurttançıkmaz

https://doi.org/10.31801/cfsuasmas.1187854

Öz

Kaynakça

  • Ali, A.T., Non-lightlike constant angle ruled surfaces in Minkowski 3-space, Journal of Geometry and Physics, 157 (2020), 1-10. https://doi.org/10.1016/j.geomphys.2020.103833
  • Gray, A., Abbena, E., Salamon, S., Modern Differential Geometry of Curves and Surfaces with Mathematica (Third Edition), Studies in Advanced Mathematics, 2006.
  • Güler, F., An approach for designing a developable and minimal ruled surfaces using the curvature theory, Int. J. Geom. Methods Mod. Phys., 18(1) (2021), 2150015. https://doi.org/10.1142/S0219887821500158
  • Hacısalihoğlu, H.H., Differential Geometry, İnönü University Faculty of Arts and Sciences Publications, Ankara, 1983.
  • Hagen, H., Pottmann, H., Divivier, A., Visualization functions on a surface, Journal of Visualization and Animation, 2 (1991), 52-58. https://doi.org/10.1002/vis.4340020205
  • Hagen, H., Stefanie, H., Schreiber, T., Visualization and computation of curvature behaviour of freeform curves and surfaces, Comput.-Aided Des., 27 (1995), 545-552. https://doi.org/10.1016/0010-4485(95)93587-P
  • Hashemian, A., Bo, P., Barton, M., Reparameterization of ruled surfaces: toward generating smooth jerk-minimized toolpaths for multi-axis flank CNC milling, Comput.-Aided Des., 127 (2020), 102868. https://doi.org/10.1016/j.cad.2020.102868
  • Körpınar, T., Ünlütürk, Y., A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space, Int. J. Nonlinear Sci. Numer. Simul., 22(7-8) (2021), 917-926. https://doi.org/10.1515/ijnsns-2019-0306
  • Kuhnel, W., Differential Geometry Curves-Surfaces-Manifolds, Wiesbaden Braunchweig, 1999.
  • Lee, W., Park, E., On curves lying on a rational normal surface scroll, J. Pure Appl. Algebra, 223(10) (2019), 4458-4476. https://doi.org/10.1016/j.jpaa.2019.01.016
  • Sabuncuoğlu, A., Differential Geometry, Nobel Publications, 2006.
  • Sağlam, D., Kalkan, Ö., Surfaces at a constant distance from the edge of regression on a surface in $E^{3}_{1}$ , Differential Geometry-Dynamical Systems, 12 (2010), 187-200.
  • Kızıltuğ, S., Tarakcı, Ö., Yaylı, Y., On the curves lying on parallel surfaces in the Euclidean 3-space $E^{3}$, Journal of Advanced Research in Dynamical and Control Systems, 5 (2013), 26-35.
  • Kızıltuğ, S., Yaylı, Y., Timelike curves on timelike parallel surfaces in Minkowski 3-space $E^{3}_{1}$ , Math. Æterna, 2 (2012), 689-700.
  • Sun, S., Yan, S., Jiang, S., Sun, Y., A high-accuracy tool path generation (HATPG) method for 5-axis flank milling of ruled surfaces with a conical cutter based on instantaneous envelope surface modelling, Comput.-Aided Des., 151 (2022), 103354. https://doi.org/10.1016/j.cad.2022.103354
  • Tarakcı, Ö., Hacısalihoğlu, H.H., Surfaces at a constant distance from the edge of regression on a surface, Applied Mathematics and Computation, 155 (2004), 81-93. https://doi.org/10.1016/S0096-3003(03)00761-6
  • Tarakcı, Ö., Surfaces at a Constant Distance from the Edge of Regression on a Surface, PhD thesis, Ankara University Institute of Science, 2002.
  • Yurttançıkmaz, S., Tarakcı, Ö., The relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface, Adv. Math. Phys., 2015 (2015), Article ID 397126, 1-6. https://doi.org/10.1155/2015/397126
  • Yurttançıkmaz, S., Tarakcı, Ö., Image curves on the parallel-like surfaces in $E^{3}$, Int. Electron. J. Geom., 16(1) (2023), 122-131. doi:10.36890/iejg.1178434
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Semra Yurttançıkmaz 0000-0001-6712-3687

Yayımlanma Tarihi 29 Aralık 2023
Gönderilme Tarihi 12 Ekim 2022
Kabul Tarihi 2 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 4

Kaynak Göster

APA Yurttançıkmaz, S. (2023). On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(4), 867-879. https://doi.org/10.31801/cfsuasmas.1187854
AMA Yurttançıkmaz S. On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2023;72(4):867-879. doi:10.31801/cfsuasmas.1187854
Chicago Yurttançıkmaz, Semra. “On the Curves Lying on Parallel-Like Surfaces of the Ruled Surface in $E^{3}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 4 (Aralık 2023): 867-79. https://doi.org/10.31801/cfsuasmas.1187854.
EndNote Yurttançıkmaz S (01 Aralık 2023) On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 4 867–879.
IEEE S. Yurttançıkmaz, “On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 4, ss. 867–879, 2023, doi: 10.31801/cfsuasmas.1187854.
ISNAD Yurttançıkmaz, Semra. “On the Curves Lying on Parallel-Like Surfaces of the Ruled Surface in $E^{3}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/4 (Aralık 2023), 867-879. https://doi.org/10.31801/cfsuasmas.1187854.
JAMA Yurttançıkmaz S. On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:867–879.
MLA Yurttançıkmaz, Semra. “On the Curves Lying on Parallel-Like Surfaces of the Ruled Surface in $E^{3}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 4, 2023, ss. 867-79, doi:10.31801/cfsuasmas.1187854.
Vancouver Yurttançıkmaz S. On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(4):867-79.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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