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- Cartan–Karlhede_algorithm abstract "The Cartan–Karlhede algorithm is a procedure for completely classifying and comparing Riemannian manifolds. Given two Riemannian manifolds of the same dimension, it is not always obvious whether they are locally isometric. Élie Cartan, using his exterior calculus with his method of moving frames, showed that it is always possible to compare the manifolds. Carl Brans developed the method further, and the first practical implementation was presented by Anders Karlhede in 1980.The main strategy of the algorithm is to take covariant derivatives of the Riemann tensor. Cartan showed that in n dimensions at most n(n+1)/2 differentiations suffice. If the Riemann tensor and its derivatives of the one manifold are algebraically compatible with the other, then the two manifolds are isometric. The Cartan–Karlhede algorithm therefore acts as a kind of generalization of the Petrov classification.The potentially large number of derivatives can be computationally prohibitive. The algorithm was implemented in an early symbolic computation engine, SHEEP, but the size of the computations proved too challenging for early computer systems to handle. Fortunately for most problems considered, far fewer derivatives than the maximum are actually required, and the algorithm is more manageable on modern computers. On the other hand, no publicly available version exists in more modern software.".
- Cartan–Karlhede_algorithm wikiPageExternalLink GRDB2.GRDBServlet.
- Cartan–Karlhede_algorithm wikiPageID "2680495".
- Cartan–Karlhede_algorithm wikiPageLength "5664".
- Cartan–Karlhede_algorithm wikiPageOutDegree "26".
- Cartan–Karlhede_algorithm wikiPageRevisionID "665418383".
- Cartan–Karlhede_algorithm wikiPageWikiLink Carl_Brans.
- Cartan–Karlhede_algorithm wikiPageWikiLink Carl_H._Brans.
- Cartan–Karlhede_algorithm wikiPageWikiLink Category:Mathematical_methods_in_general_relativity.
- Cartan–Karlhede_algorithm wikiPageWikiLink Category:Riemannian_geometry.
- Cartan–Karlhede_algorithm wikiPageWikiLink Compact_group.
- Cartan–Karlhede_algorithm wikiPageWikiLink Computer_algebra_system.
- Cartan–Karlhede_algorithm wikiPageWikiLink Covariant_derivative.
- Cartan–Karlhede_algorithm wikiPageWikiLink Curvature_invariant.
- Cartan–Karlhede_algorithm wikiPageWikiLink Definite_bilinear_form.
- Cartan–Karlhede_algorithm wikiPageWikiLink Definite_quadratic_form.
- Cartan–Karlhede_algorithm wikiPageWikiLink Exterior_derivative.
- Cartan–Karlhede_algorithm wikiPageWikiLink Fluid_solution.
- Cartan–Karlhede_algorithm wikiPageWikiLink Frame_fields_in_general_relativity.
- Cartan–Karlhede_algorithm wikiPageWikiLink General_relativity.
- Cartan–Karlhede_algorithm wikiPageWikiLink Isometry_(Riemannian_geometry).
- Cartan–Karlhede_algorithm wikiPageWikiLink Lie_group.
- Cartan–Karlhede_algorithm wikiPageWikiLink Local_isometry.
- Cartan–Karlhede_algorithm wikiPageWikiLink Lorentz_group.
- Cartan–Karlhede_algorithm wikiPageWikiLink Metric_tensor.
- Cartan–Karlhede_algorithm wikiPageWikiLink Moving_frame.
- Cartan–Karlhede_algorithm wikiPageWikiLink Moving_frames.
- Cartan–Karlhede_algorithm wikiPageWikiLink Null_dust_solution.
- Cartan–Karlhede_algorithm wikiPageWikiLink Petrov_classification.
- Cartan–Karlhede_algorithm wikiPageWikiLink Riemann_curvature_tensor.
- Cartan–Karlhede_algorithm wikiPageWikiLink Riemann_tensor.
- Cartan–Karlhede_algorithm wikiPageWikiLink Riemannian_manifold.
- Cartan–Karlhede_algorithm wikiPageWikiLink SHEEP_(symbolic_computation_system).
- Cartan–Karlhede_algorithm wikiPageWikiLink Vacuum_solution_(general_relativity).
- Cartan–Karlhede_algorithm wikiPageWikiLink Élie_Cartan.
- Cartan–Karlhede_algorithm wikiPageWikiLinkText "Cartan–Karlhede algorithm".
- Cartan–Karlhede_algorithm wikiPageWikiLinkText "Cartan–Karlhede classification".
- Cartan–Karlhede_algorithm hasPhotoCollection Cartan–Karlhede_algorithm.
- Cartan–Karlhede_algorithm subject Category:Mathematical_methods_in_general_relativity.
- Cartan–Karlhede_algorithm subject Category:Riemannian_geometry.
- Cartan–Karlhede_algorithm comment "The Cartan–Karlhede algorithm is a procedure for completely classifying and comparing Riemannian manifolds. Given two Riemannian manifolds of the same dimension, it is not always obvious whether they are locally isometric. Élie Cartan, using his exterior calculus with his method of moving frames, showed that it is always possible to compare the manifolds.".
- Cartan–Karlhede_algorithm label "Cartan–Karlhede algorithm".
- Cartan–Karlhede_algorithm sameAs Algoritmo_de_Cartan-Karlhede.
- Cartan–Karlhede_algorithm sameAs m.07xjmq.
- Cartan–Karlhede_algorithm sameAs Q5047049.
- Cartan–Karlhede_algorithm sameAs Q5047049.
- Cartan–Karlhede_algorithm wasDerivedFrom Cartan–Karlhede_algorithm?oldid=665418383.
- Cartan–Karlhede_algorithm isPrimaryTopicOf Cartan–Karlhede_algorithm.