• Corpus ID: 236965934

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. 
View PDF on arXiv

References

SHOWING 1-10 OF 22 REFERENCES

On gradient Yamabe solitons conformal to a pseudo-Euclidian space

Invariant solutions for gradient Ricci almost solitons

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…

Triviality results for compact k-Yamabe solitons

The classification of locally conformally flat Yamabe solitons

On gradient Ricci solitons conformal to a pseudo-Euclidean space

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

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

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

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

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

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…