Kantowski–Sachs metric
In general relativity the Kantowski-Sachs metric (named after Ronald Kantowski and Rainer K. Sachs) describes a homogeneous but anisotropic universe whose spatial section has the topology of 
  
    
      
        
          R
        
        ×
        
          S
          
            2
          
        
      
    
    {\displaystyle \mathbb {R} \times S^{2}}
  . The metric is:

  
    
      
        d
        
          s
          
            2
          
        
        =
        −
        d
        
          t
          
            2
          
        
        +
        
          e
          
            2
            
              
                Λ
              
            
            t
          
        
        d
        
          z
          
            2
          
        
        +
        
          
            1
            Λ
          
        
        (
        d
        
          θ
          
            2
          
        
        +
        
          sin
          
            2
          
        
        ⁡
        θ
        d
        
          ϕ
          
            2
          
        
        )
      
    
    {\displaystyle ds^{2}=-dt^{2}+e^{2{\sqrt {\Lambda }}t}dz^{2}+{\frac {1}{\Lambda }}(d\theta ^{2}+\sin ^{2}\theta d\phi ^{2})}
  The isometry group of this spacetime is 
  
    
      
        
          R
        
        ×
        S
        O
        (
        3
        )
      
    
    {\displaystyle \mathbb {R} \times SO(3)}
  . Remarkably, the isometry group does not act simply transitively on spacetime, nor does it possess a subgroup with simple transitive action.