Year 2019, Volume 7 , Issue 2, Pages 183 - 190 2019-10-15

In this paper, we characterize the de Sitter space by means of spacelike and timelike curves that fully
lies on it. For this purpose, we consider the tangential part of the second derivative of the unit speed
curve on the hypersurface, and obtain the vector equations of the geodesics. We find the geodesics as
hyperbolas, ellipses, and helices. Moreover, we give an example of null curve with constant curvature in
4−dimensional Minkowski space and we illustrate the geodesics of S11(r) × R .
De Sitter space, geodesic, curve with constant curvature
  • Baek, J., Kim, D.S. and Kim, Y. H., A characterization of the unit sphere, Amer. Math.Monthly, 110(2003), no. 9,830–833.
  • Chen, B.Y., Kim, D.S. and Kim,Y.H., New Characterizations of W-Curves, Publ. Math. Debrecen, 69 (2006), no. 4,457-472.
  • Duggal, K. L. and Bejancu, A.Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer 1996.
  • Ferrandez, A., Gimenez, A.and Lucas, P., Null helices in Lorentzian space forms, Internat. J.Modern Phys. A,16(2001), no. 30, 4845–4863.
  • Inoguchi, J. and Lee, S., Null curves in Minkowski 3-space, Int. Electron. J. Geom., 1(2008), no. 2, 40-83
  • Kim, D.S., Kim, Y.H. and Lee, J.W. A Characterization of Hyperbolic Spaces, Bull. Korean Math. Soc., 55(2018), no.4, 1103–1107
  • Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space, Int.Electron. J. Geom., 7(2014),no.1, 44-107.
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press. Inc., 1983.
  • Öztürk, E. and Yaylı, Y., W-Curves In Lorentz-Minkowski Space, Mathematical Sciences and Applications E-Notes,5(2017), no.2, 76–88.
  • Sakaki, M., Notes on null curves in Minkowski space, Turkish Journal Math, 34(2010), 417-424, doi:10.3906/mat-0812-14
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0001-6638-3233
Author: Emre ÖZTÜRK (Primary Author)
Institution: T.C. SAYIŞTAY BAŞKANLIĞI
Country: Turkey


Orcid: 0000-0003-4398-3855
Author: Yusuf YAYLI
Institution: ANKARA ÜNİVERSİTESİ
Country: Turkey


Dates

Publication Date : October 15, 2019

Bibtex @conference paper { mathenot583477, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {183 - 190}, doi = {10.36753/mathenot.583477}, title = {Elementary Approachs on De Sitter Space}, key = {cite}, author = {ÖZTÜRK, Emre and YAYLI, Yusuf} }
APA ÖZTÜRK, E , YAYLI, Y . (2019). Elementary Approachs on De Sitter Space. Mathematical Sciences and Applications E-Notes , 7 (2) , 183-190 . DOI: 10.36753/mathenot.583477
MLA ÖZTÜRK, E , YAYLI, Y . "Elementary Approachs on De Sitter Space". Mathematical Sciences and Applications E-Notes 7 (2019 ): 183-190 <https://dergipark.org.tr/en/pub/mathenot/issue/49271/583477>
Chicago ÖZTÜRK, E , YAYLI, Y . "Elementary Approachs on De Sitter Space". Mathematical Sciences and Applications E-Notes 7 (2019 ): 183-190
RIS TY - JOUR T1 - Elementary Approachs on De Sitter Space AU - Emre ÖZTÜRK , Yusuf YAYLI Y1 - 2019 PY - 2019 N1 - doi: 10.36753/mathenot.583477 DO - 10.36753/mathenot.583477 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 183 EP - 190 VL - 7 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.583477 UR - https://doi.org/10.36753/mathenot.583477 Y2 - 2019 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes Elementary Approachs on De Sitter Space %A Emre ÖZTÜRK , Yusuf YAYLI %T Elementary Approachs on De Sitter Space %D 2019 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 7 %N 2 %R doi: 10.36753/mathenot.583477 %U 10.36753/mathenot.583477
ISNAD ÖZTÜRK, Emre , YAYLI, Yusuf . "Elementary Approachs on De Sitter Space". Mathematical Sciences and Applications E-Notes 7 / 2 (October 2019): 183-190 . https://doi.org/10.36753/mathenot.583477
AMA ÖZTÜRK E , YAYLI Y . Elementary Approachs on De Sitter Space. Math. Sci. Appl. E-Notes. 2019; 7(2): 183-190.
Vancouver ÖZTÜRK E , YAYLI Y . Elementary Approachs on De Sitter Space. Mathematical Sciences and Applications E-Notes. 2019; 7(2): 190-183.