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The aim of this note is to give an explicit description of quasi-Einsteinmetrics on $\Bbb{H}^{n}\times \Bbb{R}.$ We shall construct two examples ofquasi-Einstein metrics on this manifold and then we shall prove the uniquenessof these examples. Finally, we shall describe the closed relation betweenquasi-Einstein metrics and static metrics in the quoted space.

A note on the uniqueness of quasi-Einstein metrics on $\Bbb{H}^{n}\times \Bbb{R}$