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12 pages, 316 KiB

Open AccessArticle

Modified

F (R, T^{2})

-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

by Mohd Danish Siddiqi and Fatemah Mofarreh

Axioms 2024, 13(10), 708; https://doi.org/10.3390/axioms13100708 - 14 Oct 2024

Cited by 1 | Viewed by 965

Abstract

In the present research note, we discuss the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the

F (R, T^{2})

-gravity [...] Read more.

In the present research note, we discuss the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the

F (R, T^{2})

-gravity model. Furthermore, we deal with the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to

F (R, T^{2})

-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential

U_{n}

with hyperbolic Ricci solitons in the

F (R, T^{2})

-gravity model coupled with perfect fluid and a phantom barrier. Full article

12 pages, 276 KiB

Open AccessFeature PaperArticle

Results of Hyperbolic Ricci Solitons

by Adara M. Blaga and Cihan Özgür

Symmetry 2023, 15(8), 1548; https://doi.org/10.3390/sym15081548 - 6 Aug 2023

Cited by 8 | Viewed by 1854

Abstract

We obtain some properties of a hyperbolic Ricci soliton with certain types of potential vector fields, and we point out some conditions when it reduces to a trivial Ricci soliton. We also study those soliton submanifolds whose vector fields are the tangential components of a concurrent vector field on the ambient manifold, and in particular, we show that a totally umbilical hyperbolic Ricci soliton is an Einstein manifold. We prove that if the hyperbolic Ricci soliton hypersurface of a Riemannian manifold of constant curvature and endowed with a concurrent vector field has a parallel shape operator, then it is a metallic-shaped hypersurface, and we determine some conditions for it to be minimal. Moreover, we show that it is also a pseudosymmetric hypersurface. Full article

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