Elie Joseph Cartan was an influential French mathematician, born on 9 April 1869 and died on 6 May 1951, who did fundamental work in the theory of Lie groups, in differential systems, a coordinate-free geometric formulation of partial differential equations, and in differential geometry. He also made significant contributions to general relativity and indirectly to quantum mechanics, and is widely regarded as one of the greatest mathematicians of the twentieth century. His son Henri Cartan was an influential mathematician working in algebraic topology.
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Élie Cartan
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Attributed Works
Source Maurer-Cartan Form (Wikipedia)
Conjectures Posed
Source Cartan-Hadamard conjecture (Wikipedia)
In Branch
Source Élie Cartan (Wikipedia)
Source Élie Cartan (Wikipedia)
Mentored By
Source Élie Cartan (Wikipedia)
Principal Result
Source Cartan-Dieudonne theorem (Wikipedia)
Source Cartan-Hadamard theorem, Wikipedia
Source Maurer-Cartan Form (Wikipedia)
Proofs Credited
Source Cartan-Dieudonne theorem (Wikipedia)
Source Cartan-Hadamard theorem, Wikipedia
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Nationality
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Source Élie Cartan (Wikipedia)Lead paragraph [nationality-culture]Quote, Lead paragraph [nationality-culture]
was an influential French mathematician
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1. Élie Cartan (Wikipedia)
Lead paragraph
He also made significant contributions to general relativity an
Lead paragraph [nationality-culture]
was an influential French mathematician
In Branch: Lie Theory, Lead paragraph [in-branch]
the theory of Lie groups
In Branch: Differential Geometry, Lead paragraph [in-branch 2]
differential geometry
- Mentored By: Sophus Lie, Infobox, doctoral advisor or academic advisors
View the SourceCartan-Dieudonne theorem (Wikipedia)
Principal Result: Cartan-Dieudonne Theorem, Lead sentence of the article on the result
In mathematics, the Cartan-Dieudonné theorem, named after Élie Cartan and Jean Dieudonné, establishes that every orthogonal transformation in an n-dimensional symmetric bilinear space can be described as the composition of at most n reflections.
Proofs Credited: Cartan-Dieudonne Theorem, Lead paragraph
In mathematics, the Cartan-Dieudonné theorem, named after Élie Cartan and Jean Dieudonné, establishes that every orthogonal transformation in an n-dimensional
View the SourceCartan-Hadamard theorem, Wikipedia
Principal Result: Cartan-Hadamard Theorem, Lead sentence of the article on the result
It was first proved by Hans Carl Friedrich von Mangoldt for surfaces in 1881, and independently by Jacques Hadamard in 1898. Élie Cartan generalized the theorem to Riemannian manifolds in 1928 (Helgason 1978; do Carmo 1992; Kobayashi & Nomizu 1969).
Proofs Credited: Cartan-Hadamard Theorem, Lead paragraph
In mathematics, the Cartan-Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive
View the SourceMaurer-Cartan Form (Wikipedia)
Principal Result: Maurer-Cartan Form, Lead sentence of the article on the resultQuote, Principal Result: Maurer-Cartan Form, Lead sentence of the article on the result
It was much used by Élie Cartan as a basic ingredient of his method of moving frames, and bears his name together with that of Ludwig Maurer.
Maurer-Cartan Form (Wikipedia)
Attributed Works: Maurer-Cartan Form, Lead paragraphQuote, Attributed Works: Maurer-Cartan Form, Lead paragraph
In mathematics, the Maurer-Cartan form for a Lie group G is a distinguished differential one-form on G that carries the basic infinitesimal information about
Cartan-Hadamard conjecture (Wikipedia)
Conjectures Posed: Cartan-Hadamard Conjecture, Lead sectionQuote, Conjectures Posed: Cartan-Hadamard Conjecture, Lead section
named after French mathematicians Élie Cartan and Jacques Hadamard
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