# Invariant solutions of gradient $k$-Yamabe solitons

@inproceedings{Tokura2021InvariantSO, title={Invariant solutions of gradient \$k\$-Yamabe solitons}, author={Willian Isao Tokura and Marcelo Bezerra Barboza and Elismar Batista and Priscila Marques Kai}, year={2021} }

The purpose of this paper is to study gradient k-Yamabe solitons conformal to pseudo-Euclidean space. We characterize all such solitons invariant under the action of an (n − 1)-dimensional translation group. For rotational invariant solutions, we provide the classification of solitons with null curvatures. As an application, we construct infinitely many explicit examples of geodesically complete steady gradient k-Yamabe solitons conformal to the Lorentzian space.

## References

SHOWING 1-10 OF 22 REFERENCES

### On gradient Yamabe solitons conformal to a pseudo-Euclidian space

- Mathematics, Physics
- 2018

### Invariant solutions for gradient Ricci almost solitons

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2020

In this paper we provide an ansatz that reduces a pseudo-Riemannian gradient Ricci almost soliton (PDE) into an integrable system of ODE. First, considering a warped structure with conformally flat…

### On gradient Ricci solitons conformal to a pseudo-Euclidean space

- Mathematics
- 2014

We consider gradient Ricci solitons, conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n − 1)-dimensional translation group. We provide all such…

### Remarks on scalar curvature of Yamabe solitons

- Mathematics
- 2011

In this article, we consider the scalar curvature of Yamabe solitons. In particular, we show that, with natural conditions and non-positive Ricci curvature, any complete Yamabe soliton has constant…

### Gradient Ricci Solitons with Structure of Warped Product

- Mathematics
- 2017

In this paper we consider semi-Riemannian warped product gradient Ricci solitons. We prove that the potential function depends only on the base and the fiber is necessarily Einstein manifold. We…

### On warped product gradient Yamabe solitons

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

### ON THE GLOBAL STRUCTURE OF CONFORMAL GRADIENT SOLITONS WITH NONNEGATIVE RICCI TENSOR

- Mathematics
- 2011

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product ℝ × Nn-1, or globally conformally equivalent to the Euclidean…

### Yamabe Solitons, Determinant of the Laplacian and the Uniformization Theorem for Riemann Surfaces

- Mathematics
- 2008

In this letter, we prove that non-trivial compact Yamabe solitons or breathers do not exist. In particular our proof in the two dimensional case depends only on properties of the determimant of the…