These are things named after Élie Cartan(9 April 1869 – 6 May 1951), a French mathematician.
Cartan calculus
Cartan connection, Cartan connection applications
Cartan's criterion
Cartan formalism (physics)
Cartan involution
Cartan's magic formula
Cartan matrix
Cartan's theorem
Cartan subalgebra
Cartan subgroup
Cartan's equivalence method
Einstein–Cartan theory
Cartan-Ambrose-Hicks theorem
Cartan–Brauer–Hua theorem
Cartan–Dieudonné theorem
Cartan–Hadamard theorem
Cartan–Iwahori decomposition
Cartan–Kähler theorem
Cartan–Karlhede algorithm
Cartan–Kuranishi prolongation theorem
CAT(k) space
Maurer–Cartan form
Newton–Cartan theory
Note some are after Henri Cartan, a son of E. Cartan; e.g.,
Cartan's lemma (potential theory)
Cartan seminar
Cartan's theorems A and B
