1. A note on gradient generalized quasi-Einstein manifolds.
- Author
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Huang, Guangyue and Zeng, Fanqi
- Subjects
- *
EINSTEIN manifolds , *RIEMANNIAN manifolds , *DIFFERENTIAL geometry , *MANIFOLDS (Mathematics) , *HERMITIAN symmetric spaces - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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