Differential geometry MOC

Abstract index notation

Abstract index notation is a covariant (coördinate free) notation for general tensor fields and their contractions. The notation is closely related to the Ricci calculus. Typically we use lowercase Latin indices for abstract indices.

Conventions in these notes

• In certain situations we omit abstract indices and use classical notation when it is more convenient, e.g. viewing vector fields as derivations.
• We keep slots positionally separated in any situations where we intend to use index lowering and raising.

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