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Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms

Year 2023, Volume: 16 Issue: 1, 201 - 207, 30.04.2023
https://doi.org/10.36890/iejg.1259890

Abstract

The class of isotropic submanifolds in pseudo-Riemannian manifolds is a distinguished family
of submanifolds; they have been studied by several authors. In this article we establish Chen
inequalities for isotropic immersions. An example of an isotropic immersion for which the equality
case in the Chen first inequality holds is given.

References

  • [1] Cabrerizo, J.L., Fernández, M., Gómez, J.S.: Isotropic submanifolds of pseudo-Riemannian spaces. J. Geom. Physics. 69 (2), 1915-1924 (2012).
  • [2] Chen, B.-Y.: Some pinching and classification theorems for minimal submanifolds. Archiv Math. 60, 568-578 (1993).
  • [3] Chen, B.-Y.: Some new obstructions to minimal and Lagrangian isometric immersions. Japanese J. Math. 26, 105-127 (2000).
  • [4] Ciobanu, A., Mirea, M.: New inequalities on isotropic spacelike submanfolds in psuedo-Riemannian space forms. Romanian J. Math. Comp. Sci. 11 (2), 48-52 (2021).
  • [5] Hu, Z., Li, H.: Willmore Lagrangian spheres in the complex Euclidean space Cn. Annals of Global Analysis and Geometry. 25 (1), 73–98 (2004).
  • [6] O’Neill, B.: Isotropic and Kaehler immersions. Canad. J. Math. 17, 907-915 (1965).
Year 2023, Volume: 16 Issue: 1, 201 - 207, 30.04.2023
https://doi.org/10.36890/iejg.1259890

Abstract

References

  • [1] Cabrerizo, J.L., Fernández, M., Gómez, J.S.: Isotropic submanifolds of pseudo-Riemannian spaces. J. Geom. Physics. 69 (2), 1915-1924 (2012).
  • [2] Chen, B.-Y.: Some pinching and classification theorems for minimal submanifolds. Archiv Math. 60, 568-578 (1993).
  • [3] Chen, B.-Y.: Some new obstructions to minimal and Lagrangian isometric immersions. Japanese J. Math. 26, 105-127 (2000).
  • [4] Ciobanu, A., Mirea, M.: New inequalities on isotropic spacelike submanfolds in psuedo-Riemannian space forms. Romanian J. Math. Comp. Sci. 11 (2), 48-52 (2021).
  • [5] Hu, Z., Li, H.: Willmore Lagrangian spheres in the complex Euclidean space Cn. Annals of Global Analysis and Geometry. 25 (1), 73–98 (2004).
  • [6] O’Neill, B.: Isotropic and Kaehler immersions. Canad. J. Math. 17, 907-915 (1965).
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Marius Mirea 0009-0006-3973-2892

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

Cite

APA Mirea, M. (2023). Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms. International Electronic Journal of Geometry, 16(1), 201-207. https://doi.org/10.36890/iejg.1259890
AMA Mirea M. Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms. Int. Electron. J. Geom. April 2023;16(1):201-207. doi:10.36890/iejg.1259890
Chicago Mirea, Marius. “Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 201-7. https://doi.org/10.36890/iejg.1259890.
EndNote Mirea M (April 1, 2023) Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms. International Electronic Journal of Geometry 16 1 201–207.
IEEE M. Mirea, “Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 201–207, 2023, doi: 10.36890/iejg.1259890.
ISNAD Mirea, Marius. “Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms”. International Electronic Journal of Geometry 16/1 (April 2023), 201-207. https://doi.org/10.36890/iejg.1259890.
JAMA Mirea M. Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms. Int. Electron. J. Geom. 2023;16:201–207.
MLA Mirea, Marius. “Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 201-7, doi:10.36890/iejg.1259890.
Vancouver Mirea M. Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms. Int. Electron. J. Geom. 2023;16(1):201-7.