SageManifolds: raising and lowering Lorentzian indices
 
  
 
  
 
 
 
 
 
 
    
        
        asked 8 years ago  
 
 Dox gravatar image  
 
 
 
 
 
In the reference manual of SageManifolds is shown how to calculate the curvature_form (pag. 407 of the reference).
 
However, the result is shown as Ωab, while I'd like to be able of manipulate the Ωab.
 
Question:
How can  the latter be defined?
 
Thank you.
 
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Since a and b are not tensor indices, but some labels for the set of curvature 2-forms, what do you mean by Omega^{ab} ?
eric_g gravatar imageeric_g (
    
        8 years ago
    )
The a and b indices are indices in the tangent space. Which are raised and lowered with the flat metric (compatible with the signature of the curved spacetime). In my case η=diag(−1,1,1,1), so Ω10=−Ω10.
Dox gravatar imageDox (
    
        8 years ago
    )
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