Timeline for What was the motivation for the development of modern, intrinsic, differential geometry?
Current License: CC BY-SA 4.0
12 events
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| Apr 1, 2019 at 8:49 | comment | added | Michael Bächtold | Thanks. I had a look at Cartan's Leçons sur les invariants intégraux but couldn't find anything resembling the modern approach. | |
| Mar 30, 2019 at 21:00 | comment | added | Conifold | @MichaelBächtold The linked Samelson's paper has Cartan's references, his 1922 book Leçons sur les invariants intégraux is a summary. I added a link to MacTutor's biography of Koszul that references his 1950-s papers. | |
| Mar 30, 2019 at 20:59 | history | edited | Conifold | CC BY-SA 4.0 |
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| Mar 30, 2019 at 12:01 | comment | added | Michael Bächtold | Do you know in which works precisely Cartan developed the invariant (modern) approach? Also the works of Koszul from the 1950 you mention sound interesting. Would appreciate if you could add those references. | |
| Oct 13, 2015 at 3:09 | comment | added | Alan U. Kennington | The use of upper and lower indices for contravariant and covariant was in general use by Ricci, Levi-Civita and other at least a decade or two before Einstein. What Einstein contributed was the omission of the summation symbol. | |
| May 29, 2015 at 2:01 | history | edited | Conifold | CC BY-SA 3.0 |
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| Mar 24, 2015 at 0:40 | comment | added | Conifold | There was a thread on MO, where one commenter called Einstein's summation convention "retarded", and another "beautiful". Both got lots of upvotes. mathoverflow.net/questions/18593/… | |
| Mar 24, 2015 at 0:40 | comment | added | Conifold | I had in mind string theorists, like Witten or Vafa, who use differential forms when arguing theoretically, but switch to indices for calculations with gauge fields, etc. Even in mathematics what is superior seems to depend on the purpose, people working with representations and tensor categories often favor Penrose's notation (in the diagrammatic form), but in traditional differential geometry it is almost unseen. | |
| Mar 6, 2015 at 4:39 | comment | added | user466 | Physicists, who are more often interested in computations than in proofs, were never fully sold on the invariant notation, and continue to use indices alongside it. I don't think this is accurate. Roger Penrose, who is a physicist and a mathematician, invented abstract index notation, which is coordinate-invariant but uses indices. This notation is simply superior to the alternatives. It is the standard notation among relativists today. | |
| Mar 3, 2015 at 20:45 | history | edited | Conifold | CC BY-SA 3.0 |
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| Feb 26, 2015 at 21:11 | history | edited | Conifold | CC BY-SA 3.0 |
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| Dec 4, 2014 at 1:37 | history | answered | Conifold | CC BY-SA 3.0 |