Abstract
In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with \(div^2W(\nabla f,\nabla f)=0\) is rigid. Moreover, we show that a four-dimensional radially flat gradient shrinking Ricci soliton with \(\text {div}^2W^\pm (\nabla f,\nabla f)=0\) is either Einstein or a finite quotient of \({\mathbb {R}}^4\), \({\mathbb {S}}^2\times {\mathbb {R}}^2\) or \({\mathbb {S}}^3\times {\mathbb {R}}\).
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Communicated by Young Jin Suh.
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This work is partially supported by the National Natural Science Foundation of China (Grant No. 71973130).
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Yang, F., Zhang, L. & Ma, H. On Gradient Shrinking Ricci Solitons with Radial Conditions. Bull. Malays. Math. Sci. Soc. 44, 2161–2174 (2021). https://doi.org/10.1007/s40840-020-01058-8
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DOI: https://doi.org/10.1007/s40840-020-01058-8