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Mathematical Problems in Engineering
Volume 2009, Article ID 160917, 9 pages
http://dx.doi.org/10.1155/2009/160917
Research Article

Mannheim Offsets of Ruled Surfaces

1Department of Mathematics, Education Faculty, Amasya University, 0 5189 Amasya, Turkey
2Department of Mathematics, Arts and Science Faculty, Ondokuz Mayis University, 55139 Samsun, Turkey

Received 25 November 2008; Accepted 12 February 2009

Academic Editor: Francesco Pellicano

Copyright © 2009 Keziban Orbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [15 citations]

The following is the list of published articles that have cited the current article.

  • Tanju Kahraman, Mehmet Onder, Mustafa Kazaz, and H. Huseyin Ugurlu, “Some characterizations of Mannheim partner curves in the Minkowski 3-space E-1(3),” Proceedings Of The Estonian Academy Of Sciences, vol. 60, no. 4, pp. 210–220, 2011. View at Publisher · View at Google Scholar
  • Mehmet Önder, and H. Hüseyin Uğurlu, “Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces,” Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, vol. 83, no. 2, pp. 163–169, 2013. View at Publisher · View at Google Scholar
  • Engin As, and Süleyman Şenyurt, “Some Characteristic Properties of Parallel -Equidistant Ruled Surfaces,” Mathematical Problems in Engineering, vol. 2013, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Mehmet Önder, and H. Hüseyin Uğurlu, “On the Developable Mannheim Offsets of Timelike Ruled Surfaces,” Proceedings of the National Academy of Sciences India Section A - Physical Sciences, vol. 84, no. 4, pp. 541–548, 2014. View at Publisher · View at Google Scholar
  • Mehmet Önder, and Hüseyin Uʇurlu, “On the invariants of Mannheim offsets of timelike ruled surfaces with spacelike rulings,” Asian-European Journal of Mathematics, vol. 8, no. 1, 2015. View at Publisher · View at Google Scholar
  • Gülsüm Yeliz Şentürk, and Salim Yüce, “Properties of integral invariants of the involute-evolute offsets of ruled surfaces,” International Journal of Pure and Applied Mathematics, vol. 102, no. 4, pp. 757–768, 2015. View at Publisher · View at Google Scholar
  • Gülsüm Yeliz Şentürk, and Salim Yüce, “Bertrand Offsets of Ruled Surfaces with Darboux Frame,” Results in Mathematics, vol. 72, no. 3, pp. 1151–1159, 2016. View at Publisher · View at Google Scholar
  • Mehmet Önder, and H. Hüseyin Uğurlu, “Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces,” Boletim da Sociedade Paranaense de Matemática, vol. 34, no. 1, pp. 85, 2016. View at Publisher · View at Google Scholar
  • Dae Won Yoon, “On the evolute offsets of ruled surfaces in Minkowski 3-space,” Turkish Journal of Mathematics, vol. 40, no. 3, pp. 594–604, 2016. View at Publisher · View at Google Scholar
  • Suleyman Senyurt, and Seyda Kilicoğlu, “On the Differential Geometric Elements of Mannheim Darboux Ruled Surface in E3,” Applied Mathematical Sciences, vol. 10, no. 61-64, pp. 3087–3094, 2016. View at Publisher · View at Google Scholar
  • Mehmet Önder, and H. Hüseyin Uğurlu, “On the Developable Mannheim Offsets of Spacelike Ruled Surfaces,” Iranian Journal of Science and Technology, Transactions A: Science, 2017. View at Publisher · View at Google Scholar
  • Hathout, Bekar, and Yayli, “Ruled surfaces and tangent bundle of unit 2-sphere,” International Journal of Geometric Methods in Modern Physics, vol. 14, no. 10, 2017. View at Publisher · View at Google Scholar
  • Şeyda Kılıçoğlu, and S Leyman Şenyurt, “An examination of perpendicular intersections of BFRS and MFRS in E3,” Journal of Geometry and Symmetry in Physics, vol. 48, pp. 33–45, 2018. View at Publisher · View at Google Scholar
  • Süleyman Şenyurt, and Abdussamet Çalışkan, “The quaternionic expression of ruled surfaces,” Filomat, vol. 32, no. 16, pp. 5753–5766, 2018. View at Publisher · View at Google Scholar
  • Gülsüm Yeliz Şentürk, and Salim Yüce, “On the evolute offsets of ruled surfaces using the Darboux frame,” Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, vol. 68, no. 2, pp. 1256–1264, 2019. View at Publisher · View at Google Scholar