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The mystery of Riemann’s curvature. (English. French summary) Zbl 1312.01009
The author uses some hitherto unconsidered manuscript pages by Riemann to illuminate Riemann’s mysterious ideas about the curvature tensor that Riemann had published, as Darrigol says, in a paper too short on formulae and another too short on explanatory text. He also considers what mathematicians of Riemann’s time and later (Beez, Lipschitz, Weber, Christoffel, Ricci, and Levi-Civita) have said about these papers. He concludes that Riemann’s conjecturally most likely line of argument is supported by the previously unpublished notes, and that most of the mathematicians before Levi-Civita missed the geometrical component of Riemann’s approach.
This is an important paper, and it should be read alongside A. Cogliati’s recent treatment [“Riemann’s Commentatio Mathematica, a reassessment”, Rev. Hist. Math. 20, No. 1, 73–94 (2014; Zbl 1305.01027)].

MSC:
01A55 History of mathematics in the 19th century
53-03 History of differential geometry
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