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Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds

  • Jihun Kim , Jeonghyeong Park and Bayram Şahin
Published/Copyright: December 18, 2023
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 6

ABSTRACT

It is known that the Golden space form may not be an Einstein manifold. In this paper, it is shown that the condition to be Einstein for a Golden space form is equivalent to being weakly Einstein. In addition, the partial geodesic and cyclic parallelism of the CR-submanifolds of a Golden space are examined, and the case of the constant Golden sectional curvature is determined. Moreover, the CR-submanifolds with semi-flat normal connection are studied and an inequality is obtained. The equality case of this inequality is also checked. We also consider the totally umbilical CR-submanifold of Golden Riemannian manifolds and show that such submanifolds are totally geodesic under certain conditions. Furthermore, we obtain an inequality involving the scalar curvature of CR-submanifold and check the existence of extrinsic spheres in Golden space forms.

2020 Mathematics Subject Classification: Primary 53C15; 53C25; Secondary 53C40
Keywords: Golden structure; Golden Riemannian manifold; CR-submanifold; space form; Einstein manifold

(Communicated by Tibor Macko)

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C1083957).

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Received: 2022-09-05
Accepted: 2023-02-17
Published Online: 2023-12-18

© 2023 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2023-0117
Keywords for this article
Golden structure; Golden Riemannian manifold; CR-submanifold; space form; Einstein manifold

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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