Striction Lines of Non-developable Ruled Surfaces in Euclidean 3-Space

Year 2018, Volume: 8 Issue: 1, 219 - 227, 31.03.2018

Ali Çakmak

https://doi.org/10.21597/jist.407878

Abstract

The ruled surfaces, one of the areas of interest of differential geometry, have been one of the surface

types studied by many mathematicians from the past to the present day. Similarly, some special curves which helix,

slant helix, Bertrand curve, etc. are also the curve types discussed often by mathematicians. In this paper, it will be

shown that striction lines of non-developable ruled surfaces are helix, slant helix, Bertrand or Mannheim curve in

some special cases.

Keywords

Non-developable ruled surface, line of striction, helix, Bertrand curve, Mannheim curve

Öklid-3 Uzayında Açılabilir Olmayan Regle Yüzeylerin Striksiyon Çizgileri

Abstract

Diferansiyel geometrinin ilgi alanlarından olan regle yüzeyler, geçmişten günümüze bir çok matematikçi

tarafından çalışılan yüzey tiplerinden birisidir. Benzer şekilde helis, slant helis, Bertrand eğrisi gibi bazı özel

eğriler de matematikçiler tarafından sıklıkla tartışılan eğri tipleridir. Bu makalede, bazı özel durumlarda açılabilir

olmayan regle yüzeylerin striksiyon çizgilerinin helis, slant helis, Bertrand eğrisi ya da Mannheim eğrisi olduğu

gösterilecektir.

Keywords

Açılabilir olmayan regle yüzey, striksiyon çizgisi, helis, Bertrand eğrisi, Mannheim eğrisi

References

• Izumiya S, Takeuchi N, 2003. Special Curves and Ruled Surfaces. Contributions to Algebra and Geometry, 44: 203-212.
• Kuhnel W, 2006. Differential geometry, Curves-Surfaces-Manifolds. Second Edition, American Mathematical Society, USA. 380p.
• Liu H, Wang F, 2008. Mannheim partner curves in 3-space. Journal of Geometry, 88: 120-126.
• Liu H, Yu Y, Jung SD, 2014. Invariants of non-developable ruled surfaces in Euclidean 3-space. Contrib. Algebra Geom., 55: 189-199.
• Yaylı Y, Saraçoğlu S, 2012. Different Approaches To Ruled Surfaces. SDU Journal of Science, 7 (1): 56-68
• Yoon DW, 2007. On Non-Developable Ruled Surfaces in Euclidean 3- Spaces. Indian J. pure appl. Math., 38(4): 281-290.
• Yu Y, Liu H, Jung SD, 2014. Structure and characterization of ruled surfaces in Euclidean 3-space. Applied Mathematics and Computation, 233: 252259.