Journal ArticleDOI
On gradient Ricci solitons conformal to a pseudo-Euclidean space
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In this article, the authors 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.Abstract:
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 solutions in the case of steady gradient Ricci solitons.read more
Citations
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Gradient Ricci Solitons with Structure of Warped Product
TL;DR: In this paper, the authors considered semi-Riemannian warped product gradient Ricci solitons and proved that the potential function depends only on the base and the fiber is necessarily Einstein manifold.
Journal ArticleDOI
On gradient Yamabe solitons conformal to a pseudo-Euclidian space
TL;DR: The steady gradient Yamabe solitons as discussed by the authors are conformal to an n -dimensional pseudo-Euclidean space and are invariant under the action of an n − 1 -dimensional translation group.
Journal ArticleDOI
Invariant solutions for the static vacuum equation
Benedito Leandro,Romildo Pina +1 more
TL;DR: In this article, the static vacuum Einstein space-time was considered and the spatial factor was conformal to a pseudo-Euclidean space, which is invariant under the action of a translation group.
Journal ArticleDOI
On warped product gradient Yamabe solitons
TL;DR: In this paper, the authors study gradient Yamabe solitons on top of warped product manifolds and prove triviality results in the case of a bounded warping function on a non-compact base and then, for compact base.
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On Warped product gradient Ricci Soliton
TL;DR: In this paper, it was shown that the potential function depends only on the base and the fiber of Ricci-flat Ricci solitons, and that the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an $(n-1)$-dimensional translation group.
References
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Journal ArticleDOI
On locally conformally flat gradient steady Ricci solitons
Huai-Dong Cao,Qiang Chen +1 more
TL;DR: In this paper, it was shown that the complete non-compact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.
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On Locally Conformally Flat Gradient Steady Ricci Solitons
Huai-Dong Cao,Qiang Chen +1 more
TL;DR: In this article, it was shown that the complete non-compact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.
Journal ArticleDOI
Rigidity of shrinking Ricci solitons
TL;DR: In this paper, it was shown that a Ricci soliton is rigid if and only if the Weyl conformal tensor of the Ricci tensor is harmonic, assuming that the curvature tensor has at most exponential growth.