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arXiv · 2012.13334

On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor

Huai-Dong Cao·Jiangtao Yu
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Abstract

In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons 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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Huai-Dong Cao, Jiangtao Yu. 2020-12-24. On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor. https://doi.org/10.1090/proc/15317

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