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could be encoded by differential forms. As a particular form of this, he conjectured that a closed form is exact if it integrates to zero over any submanifold without boundary, and that a submanifold without boundary is itself a boundary of another submanifold, if every closed form integrates to zero
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in
Lausanne with a focus on humanities, following his passion for literature and philosophy but learning little mathematics. On graduating from the Gymnasium in 1921 however, he decided not to continue with the Faculty of Letters in order to avoid Latin. He opted instead for the Faculty of Sciences
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on the advice of Dumas. Although he found inspiration for a thesis subject in
Poincaré, progress was slow as topology was a relatively new topic and access to the relevant literature was difficult in Lausanne. With the recommendation of Dumas, de Rham contacted Lebesgue and went to Paris for a few
268:. At the faculty he started out studying biology, physics and chemistry and no mathematics initially. While trying to learn some mathematics by himself as a tool for physics, his interest was raised and by the third year he abandoned biology to focus decisively on mathematics.
312:. Lebesgue provided de Rham with a lot of help in this period, both with his studies and supporting his first research publications. When he finished his thesis Lebesgue advised him to send it to
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247:, the main town of the district, travelling daily by train. By his own account, he was not an extraordinary student in school, where he mainly enjoyed painting and dreamed of becoming a
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295:. After graduating in 1925, de Rham remained at the University of Lausanne as an assistant to Dumas. Starting work towards completing his doctorate, he read the works of
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Following this work, de Rham made several attempts to unify forms and submanifolds into a single kind of mathematical object. He identified the ultimate notion of a
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months in 1926 and, again, for a few months in 1928. Both trips were financed by his own savings and he spent his time in Paris taking classes and studying at the
243:. He was the fifth born of the six children in the family of Léon de Rham, a constructions engineer. Georges de Rham grew up in Roche but went to school in nearby
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over it. De Rham, in his 1931 thesis, proved Cartan's conjecture by decomposing an arbitrary differential form into the sum of a closed form and some number of
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into vector subbundles which are invariant under the holonomy group, then the
Riemannian structure must decompose as a product. This result, now known as the
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In 1932 de Rham returned to the
University of Lausanne as an extraordinary professor. In 1936 he also became a professor at the
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and, in 1931, De Rham received his doctorate from the
University of Paris before a commission led by Cartan and including
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de Rham was also one of the best mountaineers in
Switzerland. As a member of the Independent High Mountain Group of
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604:. Grundlehren der mathematischen Wissenschaften. Vol. 266. Translated by Smith, F. R. With an introduction by
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In an additional part of his 1931 thesis, de Rham introduced higher-dimensional versions of the three-dimensional
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Georges de Rham speech on receiving the Prize of the City of
Lausanne (1979), cited in Burlet (2004) page 5
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951:. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Berlin: Springer-Verlag.
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and continued to hold both positions in parallel until his retirement in 1971.
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The First
Century of the International Commission on Mathematical Education
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since 1944, he opened several difficult routes, some of them in the
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At the
University he was mainly influenced by two professors,
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and related fields. His work is particularly important for
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A History of
Algebraic and Differential Topology 1900-1960
608:. (Translation of 1955 French original ed.). Berlin:
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Differentiable manifolds. Forms, currents, harmonic forms
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has classical roots, with the relation between forms and
801:"Stockhorn (Baltschiedertal): Arête S, par les 5 Tours"
366:, where he climbed routes until 1980. According to
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1181:Presidents of the International Mathematical Union
370:, in 1933 de Rham encountered on one of his hikes
528:. Thèses de l'entre-deux-guerres. Vol. 129.
492:automatically implies a product structure of the
231:Georges de Rham was born on 10 September 1903 in
435:, which are differential forms associated to a
684:Chatterji, Srishti; Ojanguren, Manuel (2010),
504:, has become a fundamental textbook result in
551:"Sur la reductibilité d'un espace de Riemann"
446:in the 1950s, generalizing (and inspired by)
8:
1166:Academic staff of the University of Lausanne
1042:Notices of the American Mathematical Society
212:; 10 September 1903 – 9 October 1990) was a
1057:(1992). "Georges de Rham 1903–1990".
1039:(1991). "Georges de Rham 1901–1990".
990:Foundations of differential geometry. Vol I
462:, while his theory of currents is basic to
37:Georges de Rham at the University of Geneva
1171:Academic staff of the University of Geneva
279:, who guided him in studying the works of
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358:and Pacheu). In 1944 he wrote a complete
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1090:MacTutor History of Mathematics Archive
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875:
873:
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826:"Miroir d'Argentine: La voie du Tunnel"
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402:initiated in the early 20th century by
422:. Cartan conjectured in 1928 that the
378:, who were climbing together near the
251:. In 1919 he moved with his family to
771:(1992). "Georges de Rham 1903–1990".
207:
7:
521:Sur l'analysis situs des variétés à
414:as well as the fact that not every
235:, a small village in the canton of
14:
1146:20th-century Swiss mathematicians
921:Introduction to Smooth Manifolds.
556:Commentarii Mathematici Helvetici
219:, known for his contributions to
342:(such as the south ridge of the
663:Hodge–de Rham spectral sequence
851:"George de Rham – mountaineer"
1:
1161:University of Lausanne alumni
1105:Mathematics Genealogy Project
855:mathshistory.st-andrews.ac.uk
502:de Rham decomposition theorem
728:Souvenirs de Georges de Rham
687:A glimpse of the de Rham era
995:John Wiley & Sons, Inc.
1197:
1156:University of Paris alumni
1141:People from Aigle District
1113:." Biographical sketch at
957:10.1007/978-3-540-74311-8
933:Geometric Measure Theory.
658:Laplace–Beltrami operator
618:10.1007/978-3-642-61752-2
600:de Rham, Georges (1984).
549:de Rham, Georges (1952).
518:de Rham, Georges (1931).
255:in a rented apartment in
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30:
1095:University of St Andrews
464:geometric measure theory
416:closed differential form
1176:Swiss mountain climbers
1060:Elemente der Mathematik
774:Elemente der Mathematik
725:Burlet, Oscar (2004),
266:University of Lausanne
173:University of Lausanne
105:University of Lausanne
1109:Barile, Margherita. "
887:. Birkhäuser Boston.
460:differential topology
400:differential topology
221:differential topology
1081:Robertson, Edmund F.
981:Kobayashi, Shoshichi
437:smooth triangulation
390:Mathematics research
329:University of Geneva
177:University of Geneva
145:Marcel Benoist Prize
1079:O'Connor, John J.;
787:10.5169/seals-43918
506:Riemannian geometry
488:The structure of a
481:and computed their
410:, who observed the
306:University of Paris
101:University of Paris
16:Swiss mathematician
949:Einstein manifolds
830:www.campticamp.org
805:www.campticamp.org
704:on 4 December 2023
569:10.1007/BF02564308
512:Major publications
490:Riemannian product
450:'s recent work on
396:differential forms
364:Miroir d'Argentine
360:climbing guidebook
119:de Rham cohomology
1085:"Georges de Rham"
966:978-3-540-74120-6
931:Herbert Federer.
693:, working paper,
456:cohomology theory
310:Collège de France
277:Dmitry Mirimanoff
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153:Scientific career
127:de Rham invariant
115:de Rham's theorem
53:10 September 1903
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741:on 4 March 2016
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372:James Alexander
257:Beaulieu Castle
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201:Georges de Rham
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394:The theory of
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858:. Retrieved
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833:. Retrieved
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808:. Retrieved
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736:the original
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468:Hodge theory
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322:Gaston Julia
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169:Institutions
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1151:Topologists
1136:1990 deaths
1131:1903 births
1037:Bott, Raoul
606:S. S. Chern
563:: 328–344.
479:lens spaces
408:Élie Cartan
368:John Milnor
356:L'Argentine
340:Valais Alps
318:Paul Montel
314:Élie Cartan
281:Émile Borel
241:Switzerland
163:Mathematics
87:Nationality
61:Switzerland
57:Roche, Vaud
1125:Categories
1020:0119.37502
919:John Lee.
745:15 October
708:16 October
669:References
644:0534.58003
593:0048.15701
534:57.1520.06
525:dimensions
49:1903-09-10
585:121784433
380:Weisshorn
354:(such as
352:Vaud Alps
344:Stockhorn
261:Gymnasium
227:Biography
987:(1963).
947:(1987).
883:(1988).
652:See also
483:homology
336:Lausanne
308:and the
301:topology
253:Lausanne
135:Holonomy
79:Lausanne
1103:at the
1012:0152974
636:0760450
577:0052177
542:3532989
444:current
362:of the
264:of the
249:painter
205:French:
131:Current
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384:Valais
350:) and
291:, and
159:Fields
147:(1965)
141:Awards
739:(PDF)
732:(PDF)
702:(PDF)
691:(PDF)
581:S2CID
426:of a
420:exact
346:from
245:Aigle
233:Roche
214:Swiss
91:Swiss
998:ISBN
961:ISBN
889:ISBN
862:2020
837:2020
812:2020
747:2015
710:2015
695:EPFL
622:ISBN
470:and
406:and
374:and
320:and
275:and
237:Vaud
68:Died
43:Born
1016:Zbl
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783:doi
640:Zbl
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530:JFM
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