Abstract
In this note, we study a gradient generalized m-quasi-Einstein manifold. That is, there exist two smooth functions f, \({\lambda}\) such that
where m is a constant. We first obtain some rigidity results on compact gradient generalized m-quasi-Einstein manifolds. Then, we obtain some classifications for the special gradient generalized m-quasi-Einstein manifolds under the assumption that the Bach tensor is flat. In particular, we obtain some even stronger results in dimension three.
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The research of the G. Huang is supported by NSFC No. 11001076, 11171091. The research of the F. Zeng is supported by NSFC No. 11401179.
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Huang, G., Zeng, F. A note on gradient generalized quasi-Einstein manifolds. J. Geom. 106, 297–311 (2015). https://doi.org/10.1007/s00022-014-0249-8
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DOI: https://doi.org/10.1007/s00022-014-0249-8