- This article is about the concept in Riemannian geometry. For the typographic concept, see Typeface#Font metrics.
||It has been suggested that this article be merged into metric connection. (Discuss) Proposed since September 2011.|
Although other covariant derivatives may be supported within the metric, usually one only ever considers the metric-compatible one. This is because given two covariant derivatives, and , there exists a tensor for transforming from one to the other:
If the space is also torsion-free, then the tensor is symmetric in its first two indices.
- Rodrigues, W. A.; Fernández, V. V.; Moya, A. M. (2005). "Metric compatible covariant derivatives". arXiv:math/0501561.
- Wald, Robert M. (1984), General Relativity, University of Chicago Press, ISBN 0-226-87033-2
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