Riemann Tensor Notation Explained | Choquet-Bruhat GR

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SUMMARY

The discussion focuses on the notation of the Riemann tensor as defined in Choquet-Bruhat's General Relativity text, specifically in the context of sectional curvature. The notation Riemann(X, Y; X, Y) is clarified to indicate that the semi-colon does not imply a derivative but rather serves to denote the Riemann tensor evaluated at the vectors X and Y. This distinction is crucial for understanding the mathematical framework of General Relativity as presented in the book.

PREREQUISITES
  • Understanding of Riemannian geometry
  • Familiarity with General Relativity concepts
  • Knowledge of vector notation in differential geometry
  • Basic grasp of curvature in mathematical physics
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  • Study the Riemann tensor properties in detail
  • Explore sectional curvature applications in cosmology
  • Learn about the implications of curvature in General Relativity
  • Review Choquet-Bruhat's GR text for deeper insights
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Hello
I have been going through the cosmology chapter in Choquet Bruhats GR and Einstein equations and in definition 3.1 of chapter 5 she defines the sectional curvature with a Riemann( X, Y;X, Y) (X and Y two vectors)
I don't understand this notation, regarding the use of the semi colon, is it a derivative or just a way of saying Riemann( X, Y, X, Y)?
 
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No derivative. That's just the Riemann tensor.
 

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