Cartan–Karlhede algorithm: Difference between revisions

Revision as of 08:36, 16 September 2005

Revision as of 08:38, 16 September 2005

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One of the most fundamental problems of [[Riemannian geometry]] is this: given two [[Riemannian manifold]]s of the same dimension, how can one tell if they are [[locally isometric'']]? This question was addressed by [[Elwin Christoffel]], and completely solved by [[Élie Cartan]] using his [[exterior derivative|exterior calculus]] with his method of [[moving frames]].

Cartan's method was adapted and improved for general relativity by A. Karlhede, who gave the first algorithmic description of what is now called the '''Cartan-Karlhede algorithm'''. The algorithm was soon implemented by J. Åman in an early symbolic computation engine, [[SHEEP (symbolic computation system)]], but the size of the computations proved too challenging for early computer systems to handle.