Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms

Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms

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.

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  • [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)