A new characterization between osculating strip curves and ruled surfaces in Lorentzian space

Yıl 2016, Cilt: 4 Sayı: 4, 101 - 113, 31.12.2016

Suha Yilmaz Yasin Unluturk

Öz

In this work, we study the conditions between
osculating strip curves and ruled surfaces in Lorentzian space. For this study,
we establish a system of differential equations characterizing both spacelike
and timelike ruled surfaces in Lorentzian space by using the invariant
quantities of osculating strip curves on the given ruled surfaces. We obtain
the solutions of these systems for special cases. Regarding to these special
solutions, we give some results of relations between osculating strip curves
and ruled surfaces in Lorentzian space.

Anahtar Kelimeler

Lorentz space, osculating strip curve, normal curve, Blaschke frame

Kaynakça

• N. Ayyıldız, A.C. Çöken, A. Yücesan, Differential-geometrical conditions between geodesic curves and ruled surfaces in the Lorentz space, Balk. J. Geo. Appl., 7(1) 2001, 1-12.
• N. Ayyıldız, A.C. Çöken, A. Kılıç, Differential-geometrical conditions between curves and semi-ruled surfaces in the semi-Euclidean spaces, Tensor N. S., 62(2) 2000, 112-119.
• W. Blaschke, Vorlesungen über differential geometrie I, Ban I , Verlag Von Julius Springer-Verlag in Berlin, 1930.
• C. Ekici, E. Özüsağlam, On the method of determination of a developable timelike ruled surface, KJSE- Kuwait Journal of Science & Engineering, 39(1A) 2012, 19-41.
• C. Ekici, A.C. Çöken, The integral invariants of parallel timelike ruled surfaces, JMAA- Journal of Mathematical Analysis and Applications, 393(1) 2012, 97-107.
• H.W. Guggenheimer, Differential geometry, Mc. Graw-Hill Book Company, New York, 1963.
• Ş. Nizamoğlu, N. Gülpınar, Differential-geometrical conditions between curves and ruled surfaces, J. Fac. Scie. Ege Uni. 16(1) 1993, 53-62.
• B. O ’Neill, Semi-Riemannian geometry with applications to relativity, Academic press Inc, London, 1983.
• Ö. Pasinli, Ruled surfaces, Master Thesis, Grad. Sch. Nat. Appl. Sci. Dokuz Eylül Uni., İzmir, 1997.
• Ü, Pekmen, Differential-geometrical conditions between geodesic curves and ruled surfaces, J. Fac. Scie. Ege Uni., 16(1), 1995, 67-74.
• E. Study, Die geometrie der dynamen, Verlag Teubner, Leipzig, 1933.
• M. Şişman, Differential geometrical conditions between curvature and osculating strip curves and ruled surfaces, Master Thesis, Grad. Sch. Nat. Appl. Sci. Dokuz Eylül Uni., İzmir, 1995.
• Tutar A. IL ^3 Lorentz uzayında küresel eğriler ve Joachimsthal teoremi, Ph D Dissertation, Ondokuz Mayıs Üniversitesi, 1994, 36–37 (in Turkish).
• H.H. Uğurlu, A. Çalışkan, Darboux ani dönme vektörleri ile spacelike ve timelike yüzeyler geometrisi, CBÜ Yay., Manisa, 2012.
• G.R. Veldkamp, On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Math. Theory, 11, 1976, 141-156.