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Year 2019, Volume: 7 Issue: 2, 183 - 190, 15.10.2019

Emre Öztürk Yusuf Yaylı

https://doi.org/10.36753/mathenot.583477

Abstract

References

  • 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

Elementary Approachs on De Sitter Space

Year 2019, Volume: 7 Issue: 2, 183 - 190, 15.10.2019

Emre Öztürk Yusuf Yaylı

https://doi.org/10.36753/mathenot.583477

Abstract

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 .

Keywords

De Sitter space geodesic curve with constant curvature

References

  • 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
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Emre Öztürk 0000-0001-6638-3233

Yusuf Yaylı 0000-0003-4398-3855

Publication Date October 15, 2019
Submission Date June 27, 2019
Acceptance Date August 18, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Öztürk, E., & Yaylı, Y. (2019). Elementary Approachs on De Sitter Space. Mathematical Sciences and Applications E-Notes, 7(2), 183-190. https://doi.org/10.36753/mathenot.583477
AMA Öztürk E, Yaylı Y. Elementary Approachs on De Sitter Space. Math. Sci. Appl. E-Notes. October 2019;7(2):183-190. doi:10.36753/mathenot.583477
Chicago Öztürk, Emre, and Yusuf Yaylı. “Elementary Approachs on De Sitter Space”. Mathematical Sciences and Applications E-Notes 7, no. 2 (October 2019): 183-90. https://doi.org/10.36753/mathenot.583477.
EndNote Öztürk E, Yaylı Y (October 1, 2019) Elementary Approachs on De Sitter Space. Mathematical Sciences and Applications E-Notes 7 2 183–190.
IEEE E. Öztürk and Y. Yaylı, “Elementary Approachs on De Sitter Space”, Math. Sci. Appl. E-Notes, vol. 7, no. 2, pp. 183–190, 2019, doi: 10.36753/mathenot.583477.
ISNAD Öztürk, Emre - Yaylı, 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.
JAMA Öztürk E, Yaylı Y. Elementary Approachs on De Sitter Space. Math. Sci. Appl. E-Notes. 2019;7:183–190.
MLA Öztürk, Emre and Yusuf Yaylı. “Elementary Approachs on De Sitter Space”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 2, 2019, pp. 183-90, doi:10.36753/mathenot.583477.
Vancouver Öztürk E, Yaylı Y. Elementary Approachs on De Sitter Space. Math. Sci. Appl. E-Notes. 2019;7(2):183-90.
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