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