[Un réexamen du Commentatio Mathematica de Riemann]
Starting with the publication of Riemann's Gesammelte Mathematische Werke in 1876, the Commentatio Mathematica has attracted considerable interest among mathematicians and historians. Nonetheless, there appears to be no consensus on the most appropriate approach to the interpretation of the paper, namely on its relationship with Riemann's Habilitationsvortrag.
This article represents a contribution to such an interesting debate. Special attention is paid to the pars secunda of Riemann's Commentatio. In particular, the focus is on the interpretation of a certain trinomial expression from which Riemann claimed that an understanding of his “curvature tensor” could be achieved.
À commencer avec la publication des œuvres de Riemann en 1876, la Commentatio Mathematica de Riemann a suscité beaucoup d'intérêt parmi les mathématiciens et les historiens. Il semble pourtant qu'aucun consensus sur la bonne lecture de ce texte en rapport avec le Habilitationsvorstrag de Riemann ne se soit dégagé. Cet article contribue à ce débat intéressant. Nous prêtons particulièrement attention à la pars secunda, nous centrons notre interprétation autour d'une certaine expression trinomiale dont Riemann prétend qu'elle permet de comprendre le « tenseur de courbure » .
Keywords: Riemann, metric geometry, tensor calculus, curvature tensor
Mots-clés : Riemann, géométrie métrique, calcul tensoriel, tenseur de courbure
@article{RHM_2014__20_1_73_0,
author = {Cogliati, Alberto},
title = {Riemann's {\protect\emph{Commentatio} {Mathematica},} a reassessment},
journal = {Revue d'histoire des math\'ematiques},
pages = {73--94},
year = {2014},
volume = {20},
number = {1},
doi = {10.24033/rhm.179},
mrnumber = {3245150},
zbl = {1305.01027},
language = {en},
url = {https://www.numdam.org/articles/10.24033/rhm.179/}
}
Cogliati, Alberto. Riemann's Commentatio Mathematica, a reassessment. Revue d'histoire des mathématiques, Tome 20 (2014) no. 1, pp. 73-94. doi: 10.24033/rhm.179
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