On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor
Differential Geometry
2024-03-12 v2
Abstract
In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify -dimensional () complete -flat gradient steady Ricci solitons. More precisely, we prove that any -dimensional complete noncompact gradient steady Ricci soliton with vanishing -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.
Keywords
Cite
@article{arxiv.2012.13334,
title = {On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor},
author = {Huai-Dong Cao and Jiangtao Yu},
journal= {arXiv preprint arXiv:2012.13334},
year = {2024}
}
Comments
10 pages; final version to appear in Proc. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1105.3163