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A covariant tensor field takes vectors as inputs and outputs a scalar number. In the context of a Riemannian metric, it operates on pairs of vectors from the tangent space at a given point.
Conditions: The tensor field is covariant.; Inputs are vectors from the tangent space.; Output is a scalar.
A covariant tensor field takes vectors as inputs and outputs a scalar number. In the context of a Riemannian metric, it operates on pairs of vectors from the tangent space at a given point.
Conditions: The tensor field is covariant.; Inputs are vectors from the tangent space.; Output is a scalar.