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Bibliographic Details
Main Authors: Cao, Huai-Dong, Yu, Jiangtao
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2012.13334
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Table of Contents:
  • 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.