Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 69 Sayı: 1, 684 - 698, 30.06.2020
https://doi.org/10.31801/cfsuasmas.487789

Öz

Kaynakça

  • Abbena, E., Salamon, S., Gray, A., Modern differential geometry of curves and surfaces with Mathematica, CRC press, 2005.
  • DoCarmo M. P., Differential geometry of curves and surfaces, Prentice Hall, Englewood, Cliffs, 1976.
  • Fenchel, W., On the Differential Geometry of Closed Space Curves, Bull. Amer. Math. Soc., 57 (1951), 44-54.
  • Güven, İ. A., Kaya, S. and Hacısalihoğlu, H. H., On closed ruled surfaces concerned with dual Frenet and Bishop frames, J. Dyn. Syst. Geom. Theor., 9(1) (2011), 67-74.
  • Gürsoy, O., The dual angle of pitch of a closed ruled surface, Mech. Mach. Theory, 25(2) (1990), 131-140.
  • Gürsoy, O., On the integral invariants of a closed ruled surface, J. Geom., 39(1) (1990), 80-91.
  • Hacısalihoğlu, H. H., On the pitch of a closed ruled surface, Mech. Mach. Theory, 7(3) (1972), 291-305.
  • Huyghens, C., Horologium ascillatorium, part III, 1963.
  • Kasap, E. and Kuruoğlu, N., The Bertrand offsets of ruled surfaces in IR₁³, Acta Math Vietnam, 31 (2006), 39-48.
  • Kasap, E., Yüce, S. and Kuruoğlu, N., The involute-evolute offsets of ruled surfaces, Iranian J. Sci. Tech. Transaction A, 33 (2009), 195-201.
  • Kaya, O. and Önder, M., New Partner Curves in The Euclidean 3-Space E³, Int. J. Geom., 6(2) (2017), 41-50.
  • Liu, H. and Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(1-2) (2008), 120-126.
  • O'neill, B., Elemantary Differential Geometry, Second Edition, Elsevier, 1996.
  • Orbay, K., Kasap, E. and Aydemir. İ., Mannheim offsets of ruled surfaces, Math Problems Engineering, Article ID 160917 (2009), 9 pages.
  • Pears, L. R., Bertrand curves in Riemannian space, J. London Math. Soc., 1-10(2) (1935), 180-183.
  • Ravani, B. and Ku, T. S., Bertrand offsets of ruled and developable surfaces, Computer-Aided Design, 23(2) (1991), 145-152.
  • Rashad, A. Abdel-Baky, An explicit characterization of dual spherical curve, Commun. Fac. Sci. Univ. Ank. Series A, 51(2) (2002), 43-49.
  • Tunçer, Y., Vectorial moments of curves in Euclidean 3-space, International Journal of Geometric Methods in Modern Physics, 14(02) (2017), 1750020.
  • Uzunoğlu, B., Gök İ. and Yaylı, Y., A new approach on curves of constant precession, Appl. Math. Comput., 275 (2016), 317-232.
  • Yaylı, Y. and Saraçoğlu, S., Some Notes on Dual Spherical Curves, Journal of Informatics and Mathematical Sciences, 3(2) (2011), 177-189.

Curves and ruled surfaces according to alternative frame in dual space

Yıl 2020, Cilt: 69 Sayı: 1, 684 - 698, 30.06.2020
https://doi.org/10.31801/cfsuasmas.487789

Öz

In this paper, the vectorial moments of the alternative vectors are expressed in terms of alternative frame. According to the new versions of these vectorial moments, the parametric equations of the closed ruled surfaces corresponding to the (^N); (^C); (^W) dual curves are given. The integral invariants of the these surfaces are computed and illustrated by presenting with examples.

Kaynakça

  • Abbena, E., Salamon, S., Gray, A., Modern differential geometry of curves and surfaces with Mathematica, CRC press, 2005.
  • DoCarmo M. P., Differential geometry of curves and surfaces, Prentice Hall, Englewood, Cliffs, 1976.
  • Fenchel, W., On the Differential Geometry of Closed Space Curves, Bull. Amer. Math. Soc., 57 (1951), 44-54.
  • Güven, İ. A., Kaya, S. and Hacısalihoğlu, H. H., On closed ruled surfaces concerned with dual Frenet and Bishop frames, J. Dyn. Syst. Geom. Theor., 9(1) (2011), 67-74.
  • Gürsoy, O., The dual angle of pitch of a closed ruled surface, Mech. Mach. Theory, 25(2) (1990), 131-140.
  • Gürsoy, O., On the integral invariants of a closed ruled surface, J. Geom., 39(1) (1990), 80-91.
  • Hacısalihoğlu, H. H., On the pitch of a closed ruled surface, Mech. Mach. Theory, 7(3) (1972), 291-305.
  • Huyghens, C., Horologium ascillatorium, part III, 1963.
  • Kasap, E. and Kuruoğlu, N., The Bertrand offsets of ruled surfaces in IR₁³, Acta Math Vietnam, 31 (2006), 39-48.
  • Kasap, E., Yüce, S. and Kuruoğlu, N., The involute-evolute offsets of ruled surfaces, Iranian J. Sci. Tech. Transaction A, 33 (2009), 195-201.
  • Kaya, O. and Önder, M., New Partner Curves in The Euclidean 3-Space E³, Int. J. Geom., 6(2) (2017), 41-50.
  • Liu, H. and Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(1-2) (2008), 120-126.
  • O'neill, B., Elemantary Differential Geometry, Second Edition, Elsevier, 1996.
  • Orbay, K., Kasap, E. and Aydemir. İ., Mannheim offsets of ruled surfaces, Math Problems Engineering, Article ID 160917 (2009), 9 pages.
  • Pears, L. R., Bertrand curves in Riemannian space, J. London Math. Soc., 1-10(2) (1935), 180-183.
  • Ravani, B. and Ku, T. S., Bertrand offsets of ruled and developable surfaces, Computer-Aided Design, 23(2) (1991), 145-152.
  • Rashad, A. Abdel-Baky, An explicit characterization of dual spherical curve, Commun. Fac. Sci. Univ. Ank. Series A, 51(2) (2002), 43-49.
  • Tunçer, Y., Vectorial moments of curves in Euclidean 3-space, International Journal of Geometric Methods in Modern Physics, 14(02) (2017), 1750020.
  • Uzunoğlu, B., Gök İ. and Yaylı, Y., A new approach on curves of constant precession, Appl. Math. Comput., 275 (2016), 317-232.
  • Yaylı, Y. and Saraçoğlu, S., Some Notes on Dual Spherical Curves, Journal of Informatics and Mathematical Sciences, 3(2) (2011), 177-189.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Abdussamet Çalışkan 0000-0002-1512-2452

Süleyman Şenyurt Bu kişi benim 0000-0003-1097-5541

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 26 Kasım 2018
Kabul Tarihi 14 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Çalışkan, A., & Şenyurt, S. (2020). Curves and ruled surfaces according to alternative frame in dual space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 684-698. https://doi.org/10.31801/cfsuasmas.487789
AMA Çalışkan A, Şenyurt S. Curves and ruled surfaces according to alternative frame in dual space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):684-698. doi:10.31801/cfsuasmas.487789
Chicago Çalışkan, Abdussamet, ve Süleyman Şenyurt. “Curves and Ruled Surfaces According to Alternative Frame in Dual Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 684-98. https://doi.org/10.31801/cfsuasmas.487789.
EndNote Çalışkan A, Şenyurt S (01 Haziran 2020) Curves and ruled surfaces according to alternative frame in dual space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 684–698.
IEEE A. Çalışkan ve S. Şenyurt, “Curves and ruled surfaces according to alternative frame in dual space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 684–698, 2020, doi: 10.31801/cfsuasmas.487789.
ISNAD Çalışkan, Abdussamet - Şenyurt, Süleyman. “Curves and Ruled Surfaces According to Alternative Frame in Dual Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 684-698. https://doi.org/10.31801/cfsuasmas.487789.
JAMA Çalışkan A, Şenyurt S. Curves and ruled surfaces according to alternative frame in dual space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:684–698.
MLA Çalışkan, Abdussamet ve Süleyman Şenyurt. “Curves and Ruled Surfaces According to Alternative Frame in Dual Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 684-98, doi:10.31801/cfsuasmas.487789.
Vancouver Çalışkan A, Şenyurt S. Curves and ruled surfaces according to alternative frame in dual space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):684-98.

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

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