Research Article
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Year 2020, , 108 - 115, 15.10.2020
https://doi.org/10.36890/iejg.595442

Abstract

Project Number

NRF-2019R1l1A1A01043457

References

  • [1] Baikoussis, C. and Blair, D. E.: Integral surfaces of Sasakian space forms. J. Geom., 43(1-2), 30–40 (1992).
  • [2] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Math. 203, Birkhäuser, Boston, Basel, Berlin, (2002).
  • [3] Calvaruso, G.: Contact Lorentzian manifolds. Differential Geom. Appl. 29 , 541-551 (2011).
  • [4] Calvaruso, G. and Perrone, D. : Contact pseudo-metric manifolds. Differential Geom. Appl. 28, 615-634 (2010).
  • [5] Cho, J. T., Inoguchi, J. and Lee, J.-E.: On slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 74, 359-367 (2006).
  • [6] Ferrandez, A.: Riemannian Versus Lorentzian submanifolds, some open problems. in proc.Workshop on Recent Topics in Differential Geometry, Santiago de Compostera 89 (Depto. Geom. y Topologia, Univ. Santiago de Compostera, 1998), 109-130.
  • [7] Inoguchi, J.: Biharmonic curves in Minkowki 3-space. International Journal of Mathematics and Mathematical Sciences , no. 21, 1365-1368 (2003).
  • [8] Lee, J.-E., Suh, Y. J. and Lee, H.: C-parallel mean curvature vector fields along slant curves in Sasakian 3-manifolds. Kyungpook Math. J. 52 , 49-59 (2012).
  • [9] Lee, J.-E.: Biharmonic spacelike curves in Lorentzian Heigenberg space. Commun. Korean Math. Soc. 33 , no. 4, 1309 –1320 (2018).
  • [10] Lee, J.-E.: Slant curves and contact magnetic curves in Sasakian Lorentzian 3-manifolds. Symmetry, 11, 784, (2019).
  • [11] O’Neill, B.: Semi-Riemannian geometry with application to relativity, Academic Press, 1983.

On Slant Curves in Sasakian Lorentzian 3-Manifolds

Year 2020, , 108 - 115, 15.10.2020
https://doi.org/10.36890/iejg.595442

Abstract

In this paper,  we study $C$-parallel mean curvature vector field and $C$-proper mean curvature vector field along a slant Frenet curve in a Sasakian Lorentzian 3-manifold. In particular, we prove that a slant Frenet curve $\gamma$ in a Sasakian Lorentzian $3$-manifold $M$ satisfying $\Delta_{\dot{\gamma}} H =0$ is a geodesic or pseudo-helix with $\kappa^2=\tau^2$. For example, we find slant pseudo-helix in Lorentzian Heisenberg 3-space.                                                                                                                                                                                

Supporting Institution

National Research Foundation of Korea (NRF)

Project Number

NRF-2019R1l1A1A01043457

Thanks

The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1l1A1A01043457).

References

  • [1] Baikoussis, C. and Blair, D. E.: Integral surfaces of Sasakian space forms. J. Geom., 43(1-2), 30–40 (1992).
  • [2] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Math. 203, Birkhäuser, Boston, Basel, Berlin, (2002).
  • [3] Calvaruso, G.: Contact Lorentzian manifolds. Differential Geom. Appl. 29 , 541-551 (2011).
  • [4] Calvaruso, G. and Perrone, D. : Contact pseudo-metric manifolds. Differential Geom. Appl. 28, 615-634 (2010).
  • [5] Cho, J. T., Inoguchi, J. and Lee, J.-E.: On slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 74, 359-367 (2006).
  • [6] Ferrandez, A.: Riemannian Versus Lorentzian submanifolds, some open problems. in proc.Workshop on Recent Topics in Differential Geometry, Santiago de Compostera 89 (Depto. Geom. y Topologia, Univ. Santiago de Compostera, 1998), 109-130.
  • [7] Inoguchi, J.: Biharmonic curves in Minkowki 3-space. International Journal of Mathematics and Mathematical Sciences , no. 21, 1365-1368 (2003).
  • [8] Lee, J.-E., Suh, Y. J. and Lee, H.: C-parallel mean curvature vector fields along slant curves in Sasakian 3-manifolds. Kyungpook Math. J. 52 , 49-59 (2012).
  • [9] Lee, J.-E.: Biharmonic spacelike curves in Lorentzian Heigenberg space. Commun. Korean Math. Soc. 33 , no. 4, 1309 –1320 (2018).
  • [10] Lee, J.-E.: Slant curves and contact magnetic curves in Sasakian Lorentzian 3-manifolds. Symmetry, 11, 784, (2019).
  • [11] O’Neill, B.: Semi-Riemannian geometry with application to relativity, Academic Press, 1983.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ji-eun Lee

Project Number NRF-2019R1l1A1A01043457
Publication Date October 15, 2020
Acceptance Date May 28, 2020
Published in Issue Year 2020

Cite

APA Lee, J.-e. (2020). On Slant Curves in Sasakian Lorentzian 3-Manifolds. International Electronic Journal of Geometry, 13(2), 108-115. https://doi.org/10.36890/iejg.595442
AMA Lee Je. On Slant Curves in Sasakian Lorentzian 3-Manifolds. Int. Electron. J. Geom. October 2020;13(2):108-115. doi:10.36890/iejg.595442
Chicago Lee, Ji-eun. “On Slant Curves in Sasakian Lorentzian 3-Manifolds”. International Electronic Journal of Geometry 13, no. 2 (October 2020): 108-15. https://doi.org/10.36890/iejg.595442.
EndNote Lee J-e (October 1, 2020) On Slant Curves in Sasakian Lorentzian 3-Manifolds. International Electronic Journal of Geometry 13 2 108–115.
IEEE J.-e. Lee, “On Slant Curves in Sasakian Lorentzian 3-Manifolds”, Int. Electron. J. Geom., vol. 13, no. 2, pp. 108–115, 2020, doi: 10.36890/iejg.595442.
ISNAD Lee, Ji-eun. “On Slant Curves in Sasakian Lorentzian 3-Manifolds”. International Electronic Journal of Geometry 13/2 (October 2020), 108-115. https://doi.org/10.36890/iejg.595442.
JAMA Lee J-e. On Slant Curves in Sasakian Lorentzian 3-Manifolds. Int. Electron. J. Geom. 2020;13:108–115.
MLA Lee, Ji-eun. “On Slant Curves in Sasakian Lorentzian 3-Manifolds”. International Electronic Journal of Geometry, vol. 13, no. 2, 2020, pp. 108-15, doi:10.36890/iejg.595442.
Vancouver Lee J-e. On Slant Curves in Sasakian Lorentzian 3-Manifolds. Int. Electron. J. Geom. 2020;13(2):108-15.