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The Cartan-Karlhede algorithm has important applications in general relativity. One reason for this is that the simpler notion of [[curvature invariant]]s fails to distinguish spacetimes as well as they distinguish [[Riemannian manifold]]s, which possess a [[metric tensor]] having [[positive definite]] [[signature]].
The method was implemented by Åman and Karlhede in special purpose symbolic computation engines such as [[SHEEP (
Cartan showed that for a four dimensional manifold, such as [[spacetime]] model in general realtivity, at most ten covariant derivatives are needed, but experience shows that far fewer are needed very often. Later researchers have lowered "ten". An important unsolved problem is to better predict how many differentiations are really neccessary for spacetimes having various properties. Faster implementations of the method are also desirable.
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[[Category:Riemannian geometry]]
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