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F. Klein, W. Blaschke
Vorlesungen über höhere GeometrieThe Mathematical Gazette, 13
(1997)
Vortrag im Rahmen des Festkolloquiums an der Universität Hannover
Partielle Differential-Gleichungen erster Ordnung, in denen die unbekannte Funktion explicite vorkommt
G. Darboux
Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré, 2
S. Lie (1875)
Allgemeine Theorie der partiellen Differentialgleichungen erster OrdnungMathematische Annalen, 9
R. Tobies, D. Rowe (1990)
Korrespondenz Felix Klein — Adolph Mayer
R Tobies (2019)
10.1007/978-3-662-58749-2Felix Klein: Visionen für Mathematik, Anwendungen und Unterricht
S. Lie (1872)
Ueber Complexe, insbesondere Linien- und Kugel-Complexe, mit Anwendung auf die Theorie partieller Differential-GleichungenMathematische Annalen, 5
(2023)
On Felix Klein ’ s Early Geometrical Works , 1869 - 1872
(1989)
The Early Geometrical Works of Felix Klein and Sophus Lie
Jesper Lützen (2004)
The mathematician sophus lie: It was the audacity of my thinkingThe Mathematical Intelligencer, 26
(2000)
The letters from Klein to Lie cited here are to be published by Springer - Verlag as Correspondence between Felix Klein and Sophus Lie , eds
Zur Theorie der Differential-Probleme
(1988)
Der Briefwechsel Sophus Lie-Felix Klein, eine Einsicht in ihre persönlichen und wis
Theorie der Transformationsgruppen. Dritter Abschnitt
Over en Classe geometriske Transformationer
Rudolf Friedrich Alfred Clebsch Versuch einer darlegung und würdigung seiner wissenschaftlichen Leistungen von einigen seiner freunde
Mathematische Annalen, 7
J. Plucker
XVII. On a new geometry of spacePhilosophical Transactions of the Royal Society of London
F. Klein, A. Mayer, R. Tobies, D. Rowe (1990)
Korrespondenz Felix Klein - Adolph Mayer : Auswahl aus den Jahren 1871-1907
(1905)
Darstellung der Berührungstransformationen in Konnexkoordinaten
B. Fritzsche (1991)
Einige anmerkungen zu Sophus Lies KrankheitHistoria Mathematica, 18
D. Rowe (2019)
Felix Klein. Visionen für Mathematik, Anwendungen und Unterricht, Renate Tobies, Springer, Heidelberg (2019), 574 pp. 55 €.Historia Mathematica, 49
J. Plucker
I. On a new geometry of spaceProceedings of the Royal Society of London
S. Lie (1874)
Begründung einer Invarianten-Theorie der Berührungs-TransformationenMathematische Annalen, 8
J. Plücker, A. Clebsch, F. Klein
Neue Geometrie des Raumes : gegründet auf die Betrachtung der geraden Linie als Raumelement
(1893)
Einleitung in die höhere Geometrie , I . Vorlesung , gehalten im Wintersemester 1892 – 93 . Aus - gearbeitet von Fr . Schilling . Göttingen , 1893 ( lithograph of handwritten copy )
Torger Holtsmark and Eldar Straume. The original letters are at the Department of Manuscripts
R. Courant (2005)
Felix KleinNaturwissenschaften, 13
A. Clebsch (1873)
Ueber ein neues Grundgebilde der analysischen Geometrie der EbeneMathematische Annalen, 6
Arild Stubhaug (2002)
The Mathematician Sophus Lie
Thomas Hawkins (2012)
Emergence of the Theory of Lie Groups
(1997)
Ferdinand Lindemann aus Hannover, der Bezwinger von π .
(2008)
Das mathematische Berlin: Historische Spuren und actuelle Szene
Thomas Hawkins (1994)
The Birth of Lie's Theory of GroupsThe Mathematical Intelligencer, 16
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
D. Rowe (2003)
Emergence of the Theory of Lie Groups : An Essay in the History of Mathematics , 1869 – 1926
Much of the mathematics with which Felix Klein and Sophus Lie are now associated (Klein’s Erlangen Program and Lie’s theory of transformation groups) is rooted in ideas they developed in their early work: the consideration of geometric objects or properties preserved by systems of transformations. As early as 1870, Lie studied particular examples of what he later called contact transformations, which preserve tangency and which came to play a crucial role in his systematic study of transformation groups and differential equations. This note examines Klein’s efforts in the 1870s to interpret contact transformations in terms of connexes and traces that interpretation (which included a false assumption) over the decades that follow. The analysis passes from Klein’s letters to Lie through Lindemann’s edition of Clebsch’s lectures on geometry in 1876, Lie’s criticism of it in his treatise on transformation groups in 1893, and the careful development of that interpretation by Dohmen, a student of Engel, in his 1905 dissertation. The now-obscure notion of connexes and its relation to Lie’s line elements and surface elements are discussed here in some detail.
Archive for History of Exact Sciences – Springer Journals
Published: Jul 1, 2023
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