Every Seifert-fibered manifold has a geometric structure … of 𝔼³, S³, H²×ℝ, S²×ℝ,S͠L₂, or Nil.
Ken’ichi OHSHIKA , Teichmüller spaces of Seifert fibered manifolds with infinite π₁ in Topology and its Applications 27 (1987), 75–93

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Every Seifert-fibered manifold has a geometric structure … of 𝔼³, S³, H²×ℝ, S²×ℝ,S͠L₂, or Nil.
Ken’ichi OHSHIKA , Teichmüller spaces of Seifert fibered manifolds with infinite π₁ in Topology and its Applications 27 (1987), 75–93