```@inproceedings{Cao2020OnCG,
author={Huai-Dong Cao and Jiangtao Yu},
year={2020}
}```
• Published 4 September 2020
• Mathematics
In this paper, we extend the work in [9] to classify n-dimensional (n ≥ 5) complete D-flat gradient steady Ricci solitons. More precisely, we prove that any n-dimensional complete noncompact gradient steady Ricci soliton with vanishing D-tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends to the shrinking case and the expanding case as well.
2 Citations

### A comparison theorem for steady Ricci solitons

• Mathematics
• 2022
. We prove that a steady gradient Ricci soliton is either Ricci ﬂat with a constant potential function, or a quotient of the product steady soliton N n − 1 × R , where N n − 1 is Ricci ﬂat, or

### Curvature estimates for 4-dimensional complete gradient expanding Ricci solitons

• Mathematics
Journal für die reine und angewandte Mathematik (Crelles Journal)
• 2022
Abstract In this paper, we derive curvature estimates for 4-dimensional complete gradient expanding Ricci solitons with nonnegative Ricci curvature (outside a compact set K). More precisely, we prove

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In this paper we prove that any n-dimensional (n ≥ 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a

• Mathematics, Physics
• 2009
In this paper, we classify n-dimensional (n>2) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact non-flat conformally flat

• Mathematics
• 2009
In the first part of the paper we derive integral curvature estimates for complete gradient shrinking Ricci solitons. Our results and the recent work in M. Fernandez-Lopez and E. Garcia-Rio, Rigidity

### On Four-Dimensional Anti-self-dual Gradient Ricci Solitons

• Mathematics
• 2011
In this note we prove that any four-dimensional half-conformally flat gradient steady Ricci soliton must be either isometric to the Bryant’s soliton (up to a scaling), or with zero Ricci curvature.

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• Mathematics
• 2014
We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete

### Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature

Our main aim in this paper is to investigate the rigidity of complete noncompact gradient steady Ricci solitons with harmonic Weyl tensor. More precisely, we prove that an n-dimensional (n ≥ 5)

• Mathematics
• 2020
In this paper, we study steady Ricci solitons with a linear decay of sectional curvature. In particular, we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional

### Rotational symmetry of Ricci solitons in higher dimensions

Let (M,g) be a steady gradient Ricci soliton of dimension n \geq 4 which has positive sectional curvature and is asymptotically cylindrical. Under these assumptions, we show that (M,g) is

### Rigidity of shrinking Ricci solitons

• Mathematics
• 2011
We show that a compact Ricci soliton is rigid if and only if the Weyl conformal tensor is harmonic. In the complete noncompact case we prove the same result assuming that the curvature tensor has at

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The Ricci flow ∂g/∂t = −2Ric(g) is an evolution equation for Riemannian metrics. It was introduced by Richard Hamilton, who has shown in several cases ([7], [8], [9]) that the flow converges, up to