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Topic: Elie Cartan

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	Cartan biography
		Elie Cartan's mother was Anne Cottaz and his father was Joseph Cartan who was a flsmith.
		Cartan became a student at the École Normale Supérieure in 1888 and obtained his doctorate in 1894.
		Cartan's recognition as a first rate mathematician came to him only in his old age; before 1930 Poincaré and Weyl were probably the only prominent mathematicians who correctly assessed his uncommon powers and depth.
	www-history.mcs.st-and.ac.uk /~history/Biographies/Cartan.html (1421 words)

	Cartan's Corner : Elie Cartan (Site not responding. Last check: 2007-10-20)
		Elie Cartan, a son of a flsmith, developed a set of extraordinary mathematical ideas that have yet to be fully exploited in the physical and technical sciences.
		Cartan was the inventor of Spinors, spaces with Torsion, a champion of Projective Geometries, and the developer of a system of calculus called
		The philosophy to be developed herein is that most visible physical measurements are recognitions of Topological Defects and that irreversibility and biological aging are expressions of Topological Evolution.
	www22.pair.com /csdc/car/carfre2.htm (219 words)

	Elie Joseph Cartan Biography \| scit_06123_package.xml
		In 1903, Cartan married Marie-Louise Bianconi, and became a professor at the University of Nancy.
		Cartan's marriage was a happy one, and it produced four children, of whom the most famous was Henri, born in 1904.
		Cartan's other two children, however, met with tragedy: Jean, a composer, died of tuberculosis when he was just 25 years old, and Louis, a physicist, was executed by the Nazis in 1943 for his activities with the French Resistance.
	www.bookrags.com /biography/elie-joseph-cartan-scit-06123 (611 words)

	Cartan, Ãlie Joseph - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-20)
		CARTAN, ÉLIE JOSEPH [Cartan, Élie Joseph], 1869-1951, French mathematician.
		The son of a village flsmith, he graduated from the École normale and taught at the universities of Montpellier, Lyons, Nancy, and finally Paris, where he was professor from 1912 to 1940.
		His son, Henri Cartan, 1904-, is also a mathematician and one of the founding members of the Bourbaki group (see Bourbaki, Nicolas).
	www.encyclopedia.com /doc/1E1-cartan-e1.html (140 words)

	AllRefer.com - Elie Joseph Cartan (Mathematics, Biography) - Encyclopedia
		Elie Joseph Cartan[AlE´ zhOzef´ kArtAN´] Pronunciation Key, 1869–1951, French mathematician.
		The son of a village flsmith, he graduated from the Ecole normale and taught at the universities of Montpellier, Lyons, Nancy, and finally Paris, where he was professor from 1912 to 1940.
		His son, Henri Cartan, 1904–, is also a mathematician and one of the founding members of the Bourbaki group (see Bourbaki, Nicolas).
	reference.allrefer.com /encyclopedia/C/Cartan-E.html (245 words)

	Research interests of Andreas Cap
		Parabolic geometries are Cartan geometries of type (G,P), where G is a (real or complex) semisimple Lie group and P is a parabolic subgroup of G. The homogeneous models G/P are the so-called generalized flag manifolds.
		Elie Cartan showed that classical projective structures, conformal structures, and three-dimensional CR structures can be equivalently described as parabolic geometries.
		This slowed down the development of the theory of Cartan geometry, but then new impact came from several directions: C. Fefferman's study of the Bergmann kernel of strictly pseudoconvex domains initiated research on invariants of CR structures and, more generally, parabolic invariant theory, see [F2].
	www.mat.univie.ac.at /~cap/research.html (2536 words)

	Biografía matemáticos:Elie Joseph Cartan (Bibliografía) (Site not responding. Last check: 2007-10-20)
		M.A. Akivis y B. Rosenfeld: Elie Cartan (1869-1951).
		Les travaux de Elie Cartan sur les groupes et algèbres de Lie, Elie Cartan, 1869-1951 (homenaje de l'Acad.
		A. Lichnerowicz: Elie Cartan, 1869-1951 (homenaje de l'Acad.
	divulgamat.ehu.es /weborriak/Historia/MateOspetsuak/CartanBiblio.asp (127 words)

	Élie Cartan - Wikipedia, the free encyclopedia
		Élie Joseph Cartan (9 April 1869 – 6 May 1951) was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications.
		Cartan was born in Dolomieu in Savoie, and became a student at the École Normale Superieure in Paris in 1888.
		With these basics — Lie groups and differential forms — he went on to produce a very large body of work, and also some general techniques such as moving frames, that were gradually incorporated into the mathematical mainstream.
	en.wikipedia.org /wiki/%C3%89lie_Cartan (659 words)

	Lie derivative
		Note that the Cartan formulation of the "Lie derivative" acting on differential forms is precisely a cohomological method.
		However Cartan's formula is defined on differential forms, whose component functions are covariant, not contravariant.
		The idea that Cartan's formula for the Lie derivative acting on forms yields the functional format for the Lorentz force as a component of the Lie derivative is mathematically correct.
	quantumfuture.net /quantum_future/lie.htm (8445 words)

	Élie Cartan (Site not responding. Last check: 2007-10-20)
		Torsion as an extension to Einstein's version of general relativity was introduced by Élie Cartan in 1922¹³.
		He recognized that the torsion was characterized by a tensor and developed a differential geometric formulation that is a predecessor of the formulation used in my group's research.
		However, my group would contend that this is not always the case, and that a nonvanishing torsion in matter-free regions of spacetime may have important cosmological effects.
	www.mrao.cam.ac.uk /~rh316/Research/cartan.html (257 words)

	Cartan, Élie (1869-1951) -- from Eric Weisstein's World of Scientific Biography
		He then went on to develop the calculus of exterior differential forms which can be applied to differential geometry.
		Cartan defined the connection and symmetric Riemann space.
		Cartan was largely responsible for the modern abstract coordinate-free approach to geometry.
	scienceworld.wolfram.com /biography/Cartan.html (69 words)

	Henri Paul Cartan Biography \| scit_06123_package.xml
		Born in 1904 in Nancy, France, Cartan went on to teach at several prominent universities in his native land: Lycée Caen, Lille, Strasbourg, Paris, and Orsay.
		As the son of Elie Cartan (who modernized differential geometry), he devoted his life to mathematics.
		Among his accomplishments (under the name Bourbaki) were more than 30 volumes on Eléments de mathématique, illustrating the axiomatic structure of modern mathematics.
	www.bookrags.com /biography/henri-paul-cartan-scit-06123 (116 words)

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