On complete gradient steady Ricci solitons with vanishing 𝐷-tensor

Cao, Huai-Dong; Yu, Jiangtao

doi:10.1090/proc/15317

On complete gradient steady Ricci solitons with vanishing $D$-tensor
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by Huai-Dong Cao and Jiangtao Yu PDF

Proc. Amer. Math. Soc. 149 (2021), 1733-1742 Request permission

Abstract:

In this paper, we extend the work by the first author and Q. Chen [Duke Math. J. 162 (2013), pp. 1149–1169] to classify $n$-dimensional ($n\ge 5$) 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.

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