ELIE JOSEPH CARTAN 1869—1951

Abstract

This chapter focuses on Elie Joseph Cartan, a famous mathematician, and his work. Cartan is one of the great architects of contemporary mathematics. Cartan's work has its roots in the theory of continuous groups. He added a great deal to this theory, to the theory of differential equations, and to geometry. He developed a theory of moving frames, which generalizes the kinematical theory of Darboux. He then defined non-holonomic spaces, of which a Riemannian space is a typical example. Much of his later work on differential geometry and group theory is of a global nature. Cartan was also able to make progress with the theory of non-compact groups and symmetric spaces. He proved that the space of a simply connected, non-compact group is the topological product of a Euclidean space and, possibly, one or more compact, simple groups.