Kock, Anders The algebraic theory of moving frames. (English) Zbl 0518.18011 Cah. Topol. Géom. Différ. 23, 347-362 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 7 Documents MSC: 18F15 Abstract manifolds and fiber bundles (category-theoretic aspects) 18C10 Theories (e.g., algebraic theories), structure, and semantics 53C20 Global Riemannian geometry, including pinching Keywords:pregroup; frame; rigid motion of space; pregroupoid; orthonormal frames of Riemannian manifold; coordinate structure Citations:Zbl 0044.045 PDFBibTeX XMLCite \textit{A. Kock}, Cah. Topologie Géom. Différ. Catégoriques 23, 347--362 (1982; Zbl 0518.18011) Full Text: Numdam EuDML References: [1] 1 R. Baer , Zur Einfuhrung des Scharbegriffs , J. Reine Angew. Math. 160 ( 1929 ), 199 - 207 . JFM 55.0084.03 · JFM 55.0084.03 [2] 2 W. Blaschke , Kinematik und Q uaternionen , D. V. W. , Berlin 1960 . Zbl 0098.34701 · Zbl 0098.34701 [3] 3 E. Cartan , Groupes finis et continus et la Géométrie differentielle , Gauthier-Villars , Paris , 1937 . · JFM 63.1227.02 [4] 4 J. Certaine , The ternary operation (a b c) = ab-1 c of a group , Bull. A. M.S. 49 ( 1943 ), 869 - 877 . Article | MR 9953 | Zbl 0061.02305 · Zbl 0061.02305 · doi:10.1090/S0002-9904-1943-08042-1 [5] 5 C. Ehresmann , Les connexions infinitésimales dans un espace fibré différentiable, Coll . Topologie Bruxelle s, C.B.R.M. 1950 . MR 42768 | Zbl 0054.07201 · Zbl 0054.07201 [6] 6 C. Ehresmann , Catégories structurées , Ann. Sci. Ec. Norm. Sup. 80 ( 1963 ), 349 - 426 . Numdam | MR 197529 | Zbl 0128.02002 · Zbl 0128.02002 [7] 7 P. Johnstone , Topos Theory , Academic Pre ss , London 1977 . MR 470019 | Zbl 0368.18001 · Zbl 0368.18001 [8] 8 M. Kelly & R. Street , Review of the elements of 2-categories , Cat. Sem. Sydney 1972 /73, Lecture Notes in Math. 420 , Springer ( 1974 ). MR 357542 | Zbl 0334.18016 · Zbl 0334.18016 [9] 9 F. Klein , Vorlesungen über nicht-euklidische Geometrie , Springer , 1928 . MR 226477 | Zbl 0157.27101 · Zbl 0157.27101 [10] 10 P. Libermann , Sur les prolongements des fibrés principaux..., Analyse Globale , Le s Pre sse s de l’Université de Montréal , 1971 . MR 356117 [11] 11 S. Mac Lane & G. Birkhoff , Algebra , MacMillan , New York , 1967 . MR 214415 | Zbl 0153.32401 · Zbl 0153.32401 [12] 12 V.V. Vagner , Ternary algebraic operations in the theory of coordinate structure s , Doklady Akad. Nauk SSSR (N. S.) 81 ( 1951 ), 981 - 984 . (In Russian). MR 46120 | Zbl 0044.04503 · Zbl 0044.04503 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.