## 12 Citations

### Perturbative solutions of the f(R)-theory of gravity in a central gravitational field and some applications

- Physics, GeologyThe European Physical Journal C
- 2018

Exact solutions of an f(R) -theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a…

### Perturbative solutions of the f(R)-theory of gravity in a central gravitational field and some applications

- Physics, GeologyThe European Physical Journal C
- 2018

Exact solutions of an f(R) -theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a…

### Cosmological Bounce and Some Other Solutions in Exponential Gravity

- PhysicsUniverse
- 2018

In this work, we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric f ( R ) gravity where the form of the…

### FRW string cosmological solutions via Hojman symmetry

- Physics
- 2020

In this paper, we find exact string cosmological solutions for FRW cosmology, by using Hojman symmetry approach. The string cosmology under consideration includes a scalar field $\psi(t)$ with the…

### (2 + 1)-dimensional f(R) gravity solutions via Hojman symmetry

- MathematicsInternational Journal of Geometric Methods in Modern Physics
- 2022

In this paper, we use the Hojman symmetry approach to find new [Formula: see text]-dimensional [Formula: see text] gravity solutions, in comparison to Noether symmetry approach. In the special case…

### Jacobi multipliers and Hojman symmetry

- MathematicsInternational Journal of Geometric Methods in Modern Physics
- 2021

The geometric intrinsic approach to Hojman symmetry is developed and use is made of the theory of the Jacobi last multipliers to find the corresponding conserved quantity for non divergence-free…

### Jacobi Multipliers in Integrability and the Inverse Problem of Mechanics

- MathematicsSymmetry
- 2021

The general theory of the Jacobi last multipliers in geometric terms is reviewed and the theory is applied to different problems in integrability and the inverse problem for one-dimensional mechanical systems.

### Reduction and integrability: a geometric perspective

- Mathematics
- 2022

A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the inﬁnitesimal symmetries and the tensor…

## References

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- Mathematics
- 2011

We perform a detailed study of the modified gravity $f(R)$ models in the light of the basic geometrical symmetries, namely Lie and Noether point symmetries, which serve to illustrate the…

### Three-fluid cosmological model using Lie and Noether symmetries

- Physics, Mathematics
- 2011

We employ a three-fluid model in order to construct a cosmological model in the Friedmann–Robertson–Walker flat spacetime, which contains three types of matter: dark energy, dark matter and a perfect…

### Unified cosmic history in modified gravity: From F ( R ) theory to Lorentz non-invariant models

- Physics
- 2010

### On exact solutions for quintessential (inflationary) cosmological models with exponential potentials

- Physics
- 2011

We ﬁrst study dark energy models with a minimally–coupled scalar ﬁeld and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class…

### NÖTHER’S SYMMETRIES IN (n+1)-DIMENSIONAL NONMINIMALLY COUPLED COSMOLOGIES

- Mathematics
- 1993

We perform a systematic analysis of nonminimally coupled cosmologies in (n+1)-dimensional homogeneous and isotropic spacetimes, searching for Nother’s symmetries and generalizing the results of our…