Research Article
BibTex RIS Cite

Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms

Year 2023, Volume: 16 Issue: 1, 244 - 253, 30.04.2023
https://doi.org/10.36890/iejg.1260464

Abstract

Spacelike and timelike isotropic submanifolds of pseudo-Riemannian spaces have interesting properties, with important applications in Mathematics and Physics. The article presents inequalities for isotropic spacelike and timelike submanifolds of pseudo-Riemannian space forms and isotropic Lorentzian submanifolds are also considered.

References

  • [1] Cabrerizo, J.L., Fernandez, M. Gomez, J.S.: Isotropic submanifolds of pseudo-Riemannian spaces. Journal of Geometry and Physics. 62, 1915- 1924 (2012).
  • [2] Chen, B.Y.: Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific. Singapore (2011).
  • [3] Chen, B.Y.: Complex extensors and Lagrangian submanifolds in indefinite complex Euclidean spaces, Bulletin of the Institute of Mathematics Academia Sinica. 31 (3), 151-179 (2003).
  • [4] Ciobanu, A., Mirea, M.: New inequalities on isotropic spacelike submanifolds in pseudo-Riemannian space forms. Romanian Journal of Mathematics and Computer Science. 11 (2), 48-52 (2021).
  • [5] Deng, S.: An improved Chen-Ricci inequality, International Electronic Journal of Geometry. 2 (2), 39-45 (2009).
  • [6] Dillen, F., Vrancken, L.: Lorentzian isotropic Lagrangian immersions, Filomat. 30 (10), 2857-2867 (2016).
  • [7] Duggal, K.L., ¸Sahin, B.: Differential geometry of lightlike submanifolds. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2010).
  • [8] O’Neill, B.: Isotropic and Kähler immersions. Canadian Journal of Mathematics. 17, 907-915 (1965).
  • [9] O’Neill, B.: Semi-Riemannian geometry. With applications to relativity. Academic Press. New York (1983)
Year 2023, Volume: 16 Issue: 1, 244 - 253, 30.04.2023
https://doi.org/10.36890/iejg.1260464

Abstract

References

  • [1] Cabrerizo, J.L., Fernandez, M. Gomez, J.S.: Isotropic submanifolds of pseudo-Riemannian spaces. Journal of Geometry and Physics. 62, 1915- 1924 (2012).
  • [2] Chen, B.Y.: Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific. Singapore (2011).
  • [3] Chen, B.Y.: Complex extensors and Lagrangian submanifolds in indefinite complex Euclidean spaces, Bulletin of the Institute of Mathematics Academia Sinica. 31 (3), 151-179 (2003).
  • [4] Ciobanu, A., Mirea, M.: New inequalities on isotropic spacelike submanifolds in pseudo-Riemannian space forms. Romanian Journal of Mathematics and Computer Science. 11 (2), 48-52 (2021).
  • [5] Deng, S.: An improved Chen-Ricci inequality, International Electronic Journal of Geometry. 2 (2), 39-45 (2009).
  • [6] Dillen, F., Vrancken, L.: Lorentzian isotropic Lagrangian immersions, Filomat. 30 (10), 2857-2867 (2016).
  • [7] Duggal, K.L., ¸Sahin, B.: Differential geometry of lightlike submanifolds. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2010).
  • [8] O’Neill, B.: Isotropic and Kähler immersions. Canadian Journal of Mathematics. 17, 907-915 (1965).
  • [9] O’Neill, B.: Semi-Riemannian geometry. With applications to relativity. Academic Press. New York (1983)
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Alexandru Cıobanu 0009-0007-8843-7870

Publication Date April 30, 2023
Acceptance Date March 29, 2023
Published in Issue Year 2023 Volume: 16 Issue: 1

Cite

APA Cıobanu, A. (2023). Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms. International Electronic Journal of Geometry, 16(1), 244-253. https://doi.org/10.36890/iejg.1260464
AMA Cıobanu A. Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms. Int. Electron. J. Geom. April 2023;16(1):244-253. doi:10.36890/iejg.1260464
Chicago Cıobanu, Alexandru. “Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 244-53. https://doi.org/10.36890/iejg.1260464.
EndNote Cıobanu A (April 1, 2023) Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms. International Electronic Journal of Geometry 16 1 244–253.
IEEE A. Cıobanu, “Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 244–253, 2023, doi: 10.36890/iejg.1260464.
ISNAD Cıobanu, Alexandru. “Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms”. International Electronic Journal of Geometry 16/1 (April 2023), 244-253. https://doi.org/10.36890/iejg.1260464.
JAMA Cıobanu A. Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms. Int. Electron. J. Geom. 2023;16:244–253.
MLA Cıobanu, Alexandru. “Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 244-53, doi:10.36890/iejg.1260464.
Vancouver Cıobanu A. Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms. Int. Electron. J. Geom. 2023;16(1):244-53.