Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 72 Sayı: 3, 650 - 662, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1127781

Öz

Kaynakça

  • Kreyszig, E., Differential Geometry, Dover Publications Inc. Courier Corporation, New York, 2013.
  • Maekawa, T., Patrikalakis, N. M., Sakkalis, T., Yu, G., Analysis and applications of pipe surfaces. Computer Aided Geometric Design, 15 (1988) 437-458.
  • Xu, Z., Feng, R., Sun, J., Analytic and algebraic properties of canal surfaces, Journal of Computational and Applied Mathematics, 195 (2006), 220–228. https://doi.org/10.1016/j.cam.2005.08.002
  • Wang, G. J., Tang, K., Tai, C. L., Parametric representation of a surface pencil with a common spatial geodesic, Computer Aided Geometric Design, 36 (5) (2004), 447–459.
  • Kasap, E., Akyıldız, F. T., Orbay, K., A generalization of surfaces family with common spatial geodesic, Appl. Math. Comput., 201 (2008), 781-789. https://doi.org/10.1016/j.amc.2008.01.016
  • Li, C. Y., Wang, R. H., Zhu, C. G., Parametric representation of a surface pencil with a common line of curvature, Computer Aided Design, 43 (9) (2011), 1110–1117.
  • Küçükkarslan, Z. Y., On a family of surfaces with common asymptotic curve in the Galilean space $G_{3}$, J. Nonlinear Sci. Appl., 9 (2016) 518–523.
  • Lopez, R., Cyclic surfaces of constant Gauss curvature, Houston J. Math., 27 (2001), 799–805.
  • Lopez, R., Surfaces of constant Gauss Curvature in Lorentz-Minkowski Three-Space, Rocky Mountain J. Math., 33 (2003) 971-993.
  • Do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice Hall, NJ, 1976.
  • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press. Boca Raton, 1998.
  • Goemans, W., Van de Woestyne, I., Twisted surfaces in Euclidean and Minkowski 3-space, In: Pure and Applied Differential Geometry Padge, Shaker Verlag Aachen, Germany, (2012), 143-151.
  • Goemans, W., Van de Woestyne, I., Twisted surfaces with null rotation axis in Minkowski 3-space, Results Math., 70(1) (2016), 81-93. https://doi.org/10.1007/s00025-015-0462-2
  • Lopez, R., Moruz, M., Translation and homothetical surfaces in Euclidean space with constant curvature, J. Korean Math. Soc., 52(3) (2015), 523-535.
  • Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turkish J. Math., 28(2) (2004), 153-163.
  • Zhao, H. Y., Wang, G. J., A new method for designing a developable surface utilizing the surface pencil through a given curve, Progress in Nature Science, 18 (2008), 105–110.
  • Ergün, E., Bayram, E., Kasap, E., Surface pencil with a common line of curvature in Minkowski 3-space, Acta Mathematica Sinica-English Series, 30(12) (2014), 2103-2118.
  • Alegre, P., Arslan, K., Carriazo, A., Murathan C., Öztürk, G., Some special types of developable ruled surface, Hacettepe Journal of Mathematics and Statistics, 39(3) (2010), 319–325.
  • Hanson, A. J., Ma, H., Parallel transport approach to curve framing, Tech. Report, 425 (1995).
  • Dede, M., Helical extension curve of a space curve, Mediterranean Journal of Mathematics, 18 (2021), 1-10.
  • Ates, F., Gok, I., Ekmekci, F., N., Yaylı, Y., Characterizations of inclined curves according to parallel transport frame in E4 and Bishop frame in E3, Konuralp Journal of Mathematics, 7(1) (2019), 16-24.
  • Bishop, R. L., There is more than one way to frame a curve, Amer. Math. Monthly 82, (1975) 246–251.
  • Bloomenthal, J., Calculation of Reference Frames Along a Space Curve, Graphics Gems, Academic Press Professional, Inc., San Diego, CA, 1990.

Developable normal surface pencil

Yıl 2023, Cilt: 72 Sayı: 3, 650 - 662, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1127781

Öz

In this paper, we introduce a new class of surfaces, called as normal surface pencil. We parameterize a normal surface pencil by using the principal normal vector $\mathbf{n}$ and the binormal vector $\mathbf{b}$ of the Frenet frame of a space curve $\alpha(s)$ as follows $\varphi(s,t)=\alpha(s)+y(s,t)\mathbf{n}+z(s,t)\mathbf{b}.$ A well known example of normal surface pencil is a canal surface. Finally, we propose the sufficient conditions of a normal surface pencil being a developable surface. Then several new examples of developable normal surface pencil are constructed from these conditions.

Kaynakça

  • Kreyszig, E., Differential Geometry, Dover Publications Inc. Courier Corporation, New York, 2013.
  • Maekawa, T., Patrikalakis, N. M., Sakkalis, T., Yu, G., Analysis and applications of pipe surfaces. Computer Aided Geometric Design, 15 (1988) 437-458.
  • Xu, Z., Feng, R., Sun, J., Analytic and algebraic properties of canal surfaces, Journal of Computational and Applied Mathematics, 195 (2006), 220–228. https://doi.org/10.1016/j.cam.2005.08.002
  • Wang, G. J., Tang, K., Tai, C. L., Parametric representation of a surface pencil with a common spatial geodesic, Computer Aided Geometric Design, 36 (5) (2004), 447–459.
  • Kasap, E., Akyıldız, F. T., Orbay, K., A generalization of surfaces family with common spatial geodesic, Appl. Math. Comput., 201 (2008), 781-789. https://doi.org/10.1016/j.amc.2008.01.016
  • Li, C. Y., Wang, R. H., Zhu, C. G., Parametric representation of a surface pencil with a common line of curvature, Computer Aided Design, 43 (9) (2011), 1110–1117.
  • Küçükkarslan, Z. Y., On a family of surfaces with common asymptotic curve in the Galilean space $G_{3}$, J. Nonlinear Sci. Appl., 9 (2016) 518–523.
  • Lopez, R., Cyclic surfaces of constant Gauss curvature, Houston J. Math., 27 (2001), 799–805.
  • Lopez, R., Surfaces of constant Gauss Curvature in Lorentz-Minkowski Three-Space, Rocky Mountain J. Math., 33 (2003) 971-993.
  • Do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice Hall, NJ, 1976.
  • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press. Boca Raton, 1998.
  • Goemans, W., Van de Woestyne, I., Twisted surfaces in Euclidean and Minkowski 3-space, In: Pure and Applied Differential Geometry Padge, Shaker Verlag Aachen, Germany, (2012), 143-151.
  • Goemans, W., Van de Woestyne, I., Twisted surfaces with null rotation axis in Minkowski 3-space, Results Math., 70(1) (2016), 81-93. https://doi.org/10.1007/s00025-015-0462-2
  • Lopez, R., Moruz, M., Translation and homothetical surfaces in Euclidean space with constant curvature, J. Korean Math. Soc., 52(3) (2015), 523-535.
  • Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turkish J. Math., 28(2) (2004), 153-163.
  • Zhao, H. Y., Wang, G. J., A new method for designing a developable surface utilizing the surface pencil through a given curve, Progress in Nature Science, 18 (2008), 105–110.
  • Ergün, E., Bayram, E., Kasap, E., Surface pencil with a common line of curvature in Minkowski 3-space, Acta Mathematica Sinica-English Series, 30(12) (2014), 2103-2118.
  • Alegre, P., Arslan, K., Carriazo, A., Murathan C., Öztürk, G., Some special types of developable ruled surface, Hacettepe Journal of Mathematics and Statistics, 39(3) (2010), 319–325.
  • Hanson, A. J., Ma, H., Parallel transport approach to curve framing, Tech. Report, 425 (1995).
  • Dede, M., Helical extension curve of a space curve, Mediterranean Journal of Mathematics, 18 (2021), 1-10.
  • Ates, F., Gok, I., Ekmekci, F., N., Yaylı, Y., Characterizations of inclined curves according to parallel transport frame in E4 and Bishop frame in E3, Konuralp Journal of Mathematics, 7(1) (2019), 16-24.
  • Bishop, R. L., There is more than one way to frame a curve, Amer. Math. Monthly 82, (1975) 246–251.
  • Bloomenthal, J., Calculation of Reference Frames Along a Space Curve, Graphics Gems, Academic Press Professional, Inc., San Diego, CA, 1990.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Mustafa Dede 0000-0003-2652-637X

Yayımlanma Tarihi 30 Eylül 2023
Gönderilme Tarihi 8 Haziran 2022
Kabul Tarihi 10 Aralık 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 3

Kaynak Göster

APA Dede, M. (2023). Developable normal surface pencil. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(3), 650-662. https://doi.org/10.31801/cfsuasmas.1127781
AMA Dede M. Developable normal surface pencil. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Eylül 2023;72(3):650-662. doi:10.31801/cfsuasmas.1127781
Chicago Dede, Mustafa. “Developable Normal Surface Pencil”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 3 (Eylül 2023): 650-62. https://doi.org/10.31801/cfsuasmas.1127781.
EndNote Dede M (01 Eylül 2023) Developable normal surface pencil. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 3 650–662.
IEEE M. Dede, “Developable normal surface pencil”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 3, ss. 650–662, 2023, doi: 10.31801/cfsuasmas.1127781.
ISNAD Dede, Mustafa. “Developable Normal Surface Pencil”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/3 (Eylül 2023), 650-662. https://doi.org/10.31801/cfsuasmas.1127781.
JAMA Dede M. Developable normal surface pencil. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:650–662.
MLA Dede, Mustafa. “Developable Normal Surface Pencil”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 3, 2023, ss. 650-62, doi:10.31801/cfsuasmas.1127781.
Vancouver Dede M. Developable normal surface pencil. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(3):650-62.

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

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