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

Abstract

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

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References in corpus (4)

• Recent Progress on Ricci Solitons
• On the nonexistence of quasi-Einstein metrics
• On the Bartnik extension problem for the static vacuum Einstein equations
• Locally conformally flat Lorentzian quasi-Einstein manifolds