nLab Élie Cartan

Élie Joseph Cartan was a French differential geometer. His results include the classification of complex semisimple Lie algebras (“Cartan classification”), extension of these results to a class of symmetric spaces, the proof of the Lie–Cartan theorem (after Serre sometimes called “Lie's third theorem”) on integration of Lie algebras to Lie groups (Lie proved just the integration to local Lie groups), the method of moving frames, the introduction of Cartan’s connection, numerous results in Riemannian geometry, results related to the formal integrability of PDEs (Cartan involutive equations, Pfaffian system), etc.

Father of Henri Cartan.

Selected writings

Introducing what came to be known as Cartan geometry via Cartan structural equations for curvature and torsion of Cartan moving frames and Cartan connections:

  • Élie Cartan, Sur une généralisation de la notion de courbure de Riemann et les espaces á torsion, C. R. Acad. Sci. 174 (1922) 593-595 .

  • Élie Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie), Annales scientifiques de l’École Normale Supérieure, Sér. 3, 40 (1923) 325-412 [doi:ASENS_1923_3_40__325_0]

as reviewed in

  • Erhard Scholz, E. Cartan’s attempt at bridge-building between Einstein and the Cosserats – or how translational curvature became to be known as “torsion”, The European Physics Journal H 44 (2019) 47-75 [doi:10.1140/epjh/e2018-90059-x]
category: people

Last revised on March 17, 2024 at 10:27:00. See the history of this page for a list of all contributions to it.