Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

THE RELATIONS BETWEEN NULL GEODESIC CURVES AND TIMELIKE RULED SURFACES IN DUAL LORENTZIAN SPACE 𝔻31

  • Unluturk, Yasin (Department of Mathematics, Kirklareli University) ;
  • Yilmaz, Suha (Buca Faculty of Education, Dokuz Eylul University) ;
  • Ekici, Cumali (Department of Mathematics-Computer, Eskisehir Osmangazi University)
  • Received : 2018.08.13
  • Accepted : 2018.10.16
  • Published : 2019.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic 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 the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

Keywords

References

  1. N. Ayyildiz, A.C. Coken, A. Yucesan, Differential-geometrical conditions between geodesic curves and ruled surfaces in the Lorentz space, Balk. J. Geo. Appl., 7(1) (2001), 1-12.
  2. N. Ayyildiz, A.C. Coken, A. Kilic, Differential-geometrical conditions between curves and semi-ruled surfaces in the semi-Euclidean spaces, Tensor N. S., 62(2) (2000), 112-119.
  3. W. Blaschke, Vorlesungen uber differential geometrie I, Ban I, Verlag Von Julius Springer-Verlag in Berlin, 1930.
  4. W. B. Bonnor, Null curves in Minkowski space-time, Tensor 20 (1969), 229-242.
  5. A.C. Coken, U. Ciftci, C. Ekici, On parallel timelike ruled surfaces with timelike rulings, Kuwait J. Sci. Eng. 35(1A) (2008), 21-32.
  6. C. Ekici, E. Ozusaglam, On the method of determination of a developable timelike ruled surface, KJSE- Kuwait Journal of Science & Engineering, 39(1A) (2012), 19-41.
  7. C. Ekici, A.C. Coken, The integral invariants of parallel timelike ruled surfaces, JMAA- Journal of Mathematical Analysis and Applications, 393(1) (2012), 97-107. https://doi.org/10.1016/j.jmaa.2012.03.014
  8. H.W. Guggenheimer, Differential geometry, Mc. Graw-Hill Book Company, New York, 1963.
  9. S. Nizamoglu, N. Gulpinar, Differential-geometrical conditions between curves and ruled surfaces, J. Fac. Scie. Ege Uni. 16(1) (1993), 53-62.
  10. B. O 'Neill, Semi-Riemannian geometry with applications to relativity, Academic press Inc, London, 1983.
  11. O. Pasinli, Ruled surfaces, Master Thesis, Grad. Sch. Nat. Appl. Sci. Dokuz Eylul Uni., Izmir, 1997.
  12. U, Pekmen, Differential-geometrical conditions between geodesic curves and ruled surfaces, J. Fac. Scie. Ege Uni., 16(1) (1995), 67-74.
  13. E. Study, Die geometrie der dynamen, Verlag Teubner, Leipzig, 1933.
  14. M. Sisman, Differential geometrical conditions between curvature and osculating strip curves and ruled surfaces, Master Thesis, Grad. Sch. Nat. Appl. Sci. Dokuz Eylul Uni., Izmir, 1995.
  15. H.H. Ugurlu, A. Caliskan, Darboux ani donme vektorleri ile spacelike ve timelike yuzeyler geometrisi, CBU Yay., Manisa, 2012.
  16. G.R. Veldkamp, On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Math. Theory, 11 (1976), 141-156. https://doi.org/10.1016/0094-114X(76)90006-9