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On the Structure Lie Operator of a Real Hypersurface in the Complex Quadric

  • Juan De Dios Pérez EMAIL logo , David Pérez-López and Young Jin Suh
Published/Copyright: December 18, 2023
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 6

ABSTRACT

The almost contact metric structure that we have on a real hypersurface M in the complex quadric Qm = SOm+2/SOmSO2 allows us to define, for any nonnull real number k, the k-th generalized Tanaka-Webster connection on M, ∇^(k) . Associated to this connection, we have Cho and torsion operators FX(k) and TX(k) , respectively, for any vector field X tangent to M. From them and for any symmetric operator B on M, we can consider two tensor fields of type (1,2) on M that we denote by BF(k) and BT(k) , respectively. We classify real hypersurfaces M in Qm for which any of those tensors identically vanishes, in the particular case of B being the structure Lie operator Lξ on M.

2020 Mathematics Subject Classification: Primary 53C15; 53B25
Keywords: Complex quadric; real hypersurface; structure Lie operator; kth generalized Tanaka-Webster connection; Lie derivative

(Communicated by Tibor Macko)

Funding statement: First author is supported by Projects PID 2020-11 6126GB-I00 from MICINN and PY20-01391 from Junta de Andalucía. Third author by grant Proj. No. NRF-2018-R1D1A1B-05040381 from National Research Foundation of Korea. The authors thank the referee for valuable suggestions to improve the paper.

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Received: 2022-09-14
Accepted: 2023-03-24
Published Online: 2023-12-18

© 2023 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2023-0113
Keywords for this article
Complex quadric; real hypersurface; structure Lie operator; kth generalized Tanaka-Webster connection; Lie derivative

Articles in the same Issue

  1. ℒ-fuzzy Annihilators in Residuated Lattices
  2. Regular Double p-Algebras: A Converse to a Katriňák Theorem and Applications
  3. Uniform Local Connectedness and Completion of Metric σ-Frames
  4. On Transcendental Regular Continued Fractions
  5. On Repdigits Which are Sums or Differences of Two k-Pell Numbers
  6. Peirce Decompositions for Evolution Algebras
  7. Generalized Anti-Symmetry Laws in Groupoids
  8. New Bounds of Cyclic Jensen’s Differences via Weighted Hadamard Inequalities with Applications
  9. Geometric Properties of Generalized Bessel Function Associated with the Exponential Function
  10. On the Attainable Set of Iterative Differential Inclusions
  11. On the Differential-Difference Sine-Gordon Equation with an Integral Type Source
  12. A Critical p(x)-Laplacian Steklov Type Problem with Weights
  13. Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm
  14. Some Approximation Properties of Operators Including Degenerate Appell Polynomials
  15. Operators that are Weakly Coercive and a Compact Perturbation
  16. On the Structure Lie Operator of a Real Hypersurface in the Complex Quadric
  17. Paracompactness and Open Relations
  18. On (Strongly) (Θ-)Discrete Homogeneous Spaces
  19. The Alpha Power Muth-G Distributions and Its Applications in Survival and Reliability Analyses
  20. Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds
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