On Bach-flat gradient shrinking Ricci solitons

Details On Bach-flat gradient shrinking Ricci solitons On Bach-flat gradient shrinking Ricci solitons

2011-05-16

arxiv.org/abs/1105.3163v3

Mathematics

Differential Geometry

v3: 19 pages; corrected typos; some additional results added in Section 5

Scientific paper

In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Guassian shrinking soliton $R^4$ or the round cylinder $S^3\times R$. More generally, for n>4, a Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Guassian shrinking soliton $R^n$ or the product $N^{n-1}\times R$, where $N^{n-1}$ is Einstein..

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