Quasi-Conformal Curvature Tensor of Generalized Sasakian-Space-Forms

Chaturvedi, B. B.; Gupta, B. K.

doi:10.22190/fumi2001089c

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…In this article, we treat a Lorentzian para-Sasakian manifold [25] (L, ψ, ς, θ, δ) as a total manifold of a Θ.…”

Section: Remarkmentioning

confidence: 99%

Properties of Anti-Invariant Submersions and Some Applications to Number Theory

Hakami,

Siddiqi

2023

Mathematics

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In this article, we investigate anti-invariant Riemannian and Lagrangian submersions onto Riemannian manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable and their fibers are not totally geodesic. As a result, they are not totally geodesic maps. The harmonicity of such submersions is also examined. We specifically prove that they are not harmonic when the Reeb vector field is horizontal. Finally, we provide an illustration of our findings and mention some number-theoretic applications for the same submersions.

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“…In this article, we treat a Lorentzian para-Sasakian manifold [25] (L, ψ, ς, θ, δ) as a total manifold of a Θ.…”

Section: Remarkmentioning

confidence: 99%

Properties of Anti-Invariant Submersions and Some Applications to Number Theory

Hakami,

Siddiqi

2023

Mathematics

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The Impact of Quasi-Conformal Curvature Tensor on Warped Product Manifolds

Chen,

Shenawy,

et al. 2024

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This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic.

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Quasi-Conformal Curvature Tensor of Generalized Sasakian-Space-Forms

Cited by 2 publications

References 11 publications

Properties of Anti-Invariant Submersions and Some Applications to Number Theory

Properties of Anti-Invariant Submersions and Some Applications to Number Theory

The Impact of Quasi-Conformal Curvature Tensor on Warped Product Manifolds

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