WorldCat Identities

Cartan, Elie 1869-1951

Overview
Works: 304 works in 1,218 publications in 7 languages and 10,103 library holdings
Genres: Records and correspondence  Bibliography  Conference papers and proceedings 
Roles: Author, Director, Author of introduction, Collector, Honoree, Editor, Other, Contributor
Classifications: QA433, 516.83
Publication Timeline
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Most widely held works about Elie Cartan
 
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Most widely held works by Elie Cartan
The theory of spinors by Elie Cartan( Book )

45 editions published between 1947 and 2012 in English and Russian and held by 841 WorldCat member libraries worldwide

The French mathematician Élie Cartan (1869{u2013}1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity. One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value
Leçons sur la géométrie des espaces de Riemann by Elie Cartan( Book )

78 editions published between 1921 and 1988 in 4 languages and held by 631 WorldCat member libraries worldwide

Leçons sur les invariants intégraux by Elie Cartan( Book )

59 editions published between 1922 and 2005 in 5 languages and held by 427 WorldCat member libraries worldwide

Les systèmes differentiels extérieurs et leur applications géométriques by Elie Cartan( Book )

39 editions published between 1945 and 1971 in French and English and held by 350 WorldCat member libraries worldwide

La théorie des groupes finis et continus et la géométrie différentielle, traitées par la méthode du repere mobile. Leçons professées à la Sorbonne by Elie Cartan( Book )

45 editions published between 1937 and 1963 in 3 languages and held by 346 WorldCat member libraries worldwide

Leçons sur la géométrie projective complexe by Elie Cartan( Book )

32 editions published between 1931 and 1950 in 3 languages and held by 338 WorldCat member libraries worldwide

Leçons sur la théorie des espaces à connexion projective by Elie Cartan( Book )

20 editions published between 1937 and 1957 in 3 languages and held by 274 WorldCat member libraries worldwide

Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927 by Elie Cartan( Book )

24 editions published in 2001 in 3 languages and held by 263 WorldCat member libraries worldwide

Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition
Geometry of Riemannian spaces by Elie Cartan( Book )

8 editions published in 1983 in English and held by 240 WorldCat member libraries worldwide

Leçons sur la théorie des spineurs ... by Elie Cartan( Book )

39 editions published between 1938 and 1939 in French and English and held by 237 WorldCat member libraries worldwide

Œuvres complètes by Elie Cartan( Book )

in French and held by 205 WorldCat member libraries worldwide

Les espaces de Finsler by Elie Cartan( Book )

15 editions published in 1934 in French and held by 201 WorldCat member libraries worldwide

La topologie des groupes de Lie by Elie Cartan( Book )

18 editions published in 1936 in French and held by 191 WorldCat member libraries worldwide

La théorie des groupes finis et continus et l'analysis situs by Elie Cartan( Book )

21 editions published between 1929 and 1952 in French and Undetermined and held by 172 WorldCat member libraries worldwide

La méthode du repère mobile, la théorie des groupes continus et les espaces généralisés by Elie Cartan( Book )

21 editions published between 1933 and 1935 in French and held by 170 WorldCat member libraries worldwide

On manifolds with an affine connection and the theory of general relativity by Elie Cartan( Book )

8 editions published in 1986 in English and held by 150 WorldCat member libraries worldwide

Oeuvres complètes by Elie Cartan( Book )

42 editions published between 1955 and 1984 in 3 languages and held by 139 WorldCat member libraries worldwide

Le parallélisme absolu et la théorie unitaire du champ by Elie Cartan( Book )

12 editions published between 1932 and 1997 in French and held by 138 WorldCat member libraries worldwide

La géométrie des espaces de Riemann by Elie Cartan( Book )

13 editions published between 1925 and 1951 in French and Undetermined and held by 136 WorldCat member libraries worldwide

Exposés de géométrie by Elie Cartan( Book )

18 editions published in 1971 in 3 languages and held by 134 WorldCat member libraries worldwide

 
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Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927
Alternative Names
Cartan É.

Cartan É. 1869-1951

Cartan, E. (Elie), 1869-1951

Cartan, Élie

Cartan, Élie 1869-1951

Cartan, Élie J. 1869-1951

Cartan, Élie Joseph

Cartan, Élie Joseph 1869-1951

Cartan, M. É. 1869-1951

Élie Cartan Frans wiskundige

Élie Cartan fransk matematikar

Élie Cartan fransk matematiker

Élie Cartan französischer Mathematiker, der Beiträge zur Theorie der Lie-Gruppen und ihrer Anwendungen lieferte

Élie Cartan French mathematician

Élie Cartan mathématicien français

Élie Joseph Cartan matematico francese

Elie Kartan

Kartan, È.

Kartan, Ėli

Kartan, Ėli 1869-1951

Елі Жозеф Картан

Картан Э

Картан Э. 1869-1951

Картан Э.Д

Картан Э.Д. 1869-1951

Картан, Эли.

Эли Картан

Էլի Ժոսեֆ Կարտան

אלי קרטן

الی کارتان ریاضی‌دان فرانسوی

إيلي كارتن

এলি কারতঁ

엘리 카르탕

エリ・カルタン

カルタン, エリー

埃利·嘉当

Languages
French (471)

English (118)

Russian (9)

Japanese (4)

Italian (3)

German (2)

Swedish (2)

Covers
Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 1926-1927