An Examination Perpendicular Transversal Intersection of IFRS and MFRS E^3

Year 2018, Volume: 9, 71 - 79, 28.12.2018

Süleyman Şenyurt Şeyda Kılıçoğlu

Abstract

The surface-surface intersection (SSI) problems is very
important subject in geometry. We examined 
perpendicular transversal intersection problems of  eight Frenet ruled surfaces which are called
‘Involute Frenet ruled surfaces  (IFRS) and  
Mannheim Frenet ruled surfaces 
(MFRS) ‘ of  a curve α,  in terms of 
the  Frenet apparatus  of curve α. First using only one matrix and
orthogonality conditions of  the eight
normal  vector fieldsare given. Further
perpendicular transversal intersection conditations and curves if there exist
of eight IFRS and MFRS are examined .

Keywords

involute curves, Mannheim curves

References

• Duldul Uyar, B., Çalışkan, M., On the geodesic torsion of tangential intersection curve of two surfaces in IR3, Acta Math. Univ. Comenianae, 2(2013), 177–189.
• Ergüt, M., Körpınar, T., Turhan, E., On Normal Ruled Surfaces of General Helices In The Sol Space S ol3, TWMS J. Pure Appl. Math., 4(2)(2013), 125–130.
• Graves, L.K., Codimension one isometric immersions between Lorentz spaces, Trans. Amer. Math. Soc., 252(1979), 367–392.
• Hacisalihoğlu, H.H., Differential Geometry (in Turkish), İnçnü University Publish, 1, 1994.
• Izumiya, S., Takeuchi, N., Special Curves and Ruled Surfaces, Beitræge zur Algebra und Geometrie Contributions to Algebra and Geometry, 44(1)(2003), 203–212.
• Kılıçoğlu, Ş ., An Examination on the Mannheim Frenet ruled surface based on Norml vecr fields in E3, Konuralp Journal of Mathematics, 4(2)(2016), 223–229.
• Kılıçoğlu, Ş ., Senyurt, S., Hacisalihoğlu, H.H., An Examination on the Positions of Frenet Ruled Surfaces Along Bertrand Pairs and According to Their Normal Vector Fields in E3: Applied Mathematical Sciences, 9(142)(2015), 7095–7103.
• Orbay, K., Kasap, E., On Mannheim partner curves in 3 E, International Journal of Physical Sciences,4(5)(2009), 261–264.
• Lipschutz, M.M., Dierential Geometry, Schaum’s Outlines, 1969.
• Liu, H., Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(2008), 120–126.
• Kılıcoglu, S., Some Results on Frenet Ruled Surfaces Along the Evolute-Involute Curves, Based on Normal Vector Fields in E3, Geom. Integrability & Quantization, (2016), 296–308, doi:10.7546/giq-17-2016-296-308.
• Senyurt, S., Kılıcoglu, Ş., On the differential geometric elements of the involute ˜D scroll, Adv. Appl. Clifford Algebras,25(4)(2015), 977– 988,doi:10.1007/s00006-015-0535-z.
• Wu, S.T., Alessio, O., Costa, S.I.R., On estimating local geometric properties of intersection curves, In Proceedings of SIBGRAPI, (2000), 152–159.