Gradient Ricci-harmonic solitons on doubly warped product manifolds

Karaca, Fatma; Özgur, Cihan

doi:10.2298/fil2318969k

Filomat

2023

DOI: 10.2298/fil2318969k

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Gradient Ricci-harmonic solitons on doubly warped product manifolds

Fatma Karaca,

Cihan Özgur

Abstract: We give necessary and sufficient conditions for doubly warped product manifolds to be gradient Ricci-harmonic solitons. We also give a physical application for this kind of solitons.

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2024

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Cited by 5 publications

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Doubly warped product manifolds: Investigations through the projective curvature tensor and relativistic applications

Syied,

Chand De,

Turki

et al. 2024

AIP Advances

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This paper introduces a description of a doubly warped product manifold, taking into account certain conditions related to the projective curvature tensor. We demonstrate that the factor manifolds of a projectively flat (symmetric) doubly warped product manifold possess constant sectional curvature. In the flatness scenario, a doubly warped product manifold reduces to a singly warped product manifold. We establish that the factor manifolds of a doubly warped product manifold with harmonic projective curvature tensor are Einstein manifolds and exhibit harmonic projective curvature tensor. In Sec. VI, we provide evidence that a projectively flat (symmetric) generalized Robertson–Walker space-time is both a perfect fluid and static.

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Doubly warped product manifolds: Investigations through the projective curvature tensor and relativistic applications

Syied,

Chand De,

Turki

et al. 2024

AIP Advances

View full text Add to dashboard Cite

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Hyperbolic Ricci solitons on sequential warped product manifolds

Açıkgöz,

Özgür

2024

Filomat

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

Chen,

Shenawy,

et al. 2024

Axioms

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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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Gradient Ricci-harmonic solitons on doubly warped product manifolds

Abstract: We give necessary and sufficient conditions for doubly warped product manifolds to be gradient Ricci-harmonic solitons. We also give a physical application for this kind of solitons.

Cited by 5 publications

References 31 publications

Doubly warped product manifolds: Investigations through the projective curvature tensor and relativistic applications

Doubly warped product manifolds: Investigations through the projective curvature tensor and relativistic applications

Hyperbolic Ricci solitons on sequential warped product manifolds

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

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