# On complete gradient steady Ricci solitons with vanishing 𝐷-tensor

@inproceedings{Cao2020OnCG, title={On complete gradient steady Ricci solitons with vanishing 𝐷-tensor}, author={Huai-Dong Cao and Jiangtao Yu}, year={2020} }

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

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. 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

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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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