A note on generalized quasi‐Einstein manifolds |
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Authors: | YiHua Deng |
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Affiliation: | Department of Mathematical and Computational Sciences, Hengyang Normal University, Hengyang, P. R. China |
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Abstract: | In this note, we get a necessary and sufficient condition such that the scalar curvature of generalized m‐quasi‐Einstein manifold with is constant. In particular, we discuss a class of generalized quasi‐Einstein manifolds which are more general than ‐quasi‐Einstein manifolds and prove that these manifolds with dimension four are either Einstein or locally conformally flat under some suitable conditions. |
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Keywords: | Generalized quasi‐Einstein manifolds Weyl tensor anti‐self‐dual manifolds Einstein manifold 53C21 53C25 |
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