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Martin Gisser
Martin Gisser
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1.) The algebraic Bianchi identityalgebraic Bianchi identity must have been known to Riemann, as shown by his posthumously published prize essay to the Paris academy, "Commentatio mathematica ...". Cf. Spivak Vol. II which has an english translation and modern interpretation. (Interesting for German readers: Anmerkungen by Dedekind and Weber in "Bernhard Riemann's gesammelte Mathematische Werke" 1876, 2.Aufl. 1892, p.405ff.)

I haven't checked Delanoe's reference toFirst explicit public appearance with proof is in:

E.B. Christoffel: "Über die Transformation der homogenen Differentialausdrücke zweiten Grades", J. reine angew. Math 70 (1869) 46-70 which should contain the first published proof.

Formula $(16^d)$ on p.55 (via Göttinger Digitalisierungszentrum)

2.) The differential Bianchi identitydifferential Bianchi identity is due to Ricci. Paraphrasing a footnote in Levi-Civita's "The Absolute Tensor Calculus" (1928/1947) p.182: It was first published without proof by Padova (*) 1889 on the strength of a verbal communication by Ricci. Then it was forgotten even by Ricci himself. Bianchi rediscovered it and published a proof in 1902.

(*) E.Padova: "Sulle deformazioni infinitesime: nota", Atti della Reale Accademia dei Lincei, Rendiconti (1889) Serie 4, Volume 5, 1° Semestre, 174-178

See p.176 footnote (1) (via archive.org)

1.) The algebraic Bianchi identity must have been known to Riemann, as shown by his posthumously published prize essay to the Paris academy, "Commentatio mathematica ...". Cf. Spivak Vol. II which has an english translation and modern interpretation. (Interesting for German readers: Anmerkungen by Dedekind and Weber in "Bernhard Riemann's gesammelte Mathematische Werke" 1876, 2.Aufl. 1892, p.405ff.)

I haven't checked Delanoe's reference to Christoffel, J. reine angew. Math 70 (1869) 46-70 which should contain the first published proof.

2) The differential Bianchi identity is due to Ricci. Paraphrasing a footnote in Levi-Civita's "The Absolute Tensor Calculus" (1928/1947) p.182: It was first published without proof by Padova 1889 on the strength of a verbal communication by Ricci. Then it was forgotten even by Ricci himself. Bianchi rediscovered it and published a proof in 1902.

1.) The algebraic Bianchi identity must have been known to Riemann, as shown by his posthumously published prize essay to the Paris academy, "Commentatio mathematica ...". Cf. Spivak Vol. II which has an english translation and modern interpretation. (Interesting for German readers: Anmerkungen by Dedekind and Weber in "Bernhard Riemann's gesammelte Mathematische Werke" 1876, 2.Aufl. 1892, p.405ff.)

First explicit public appearance with proof is in:

E.B. Christoffel: "Über die Transformation der homogenen Differentialausdrücke zweiten Grades", J. reine angew. Math 70 (1869) 46-70

Formula $(16^d)$ on p.55 (via Göttinger Digitalisierungszentrum)

2.) The differential Bianchi identity is due to Ricci. Paraphrasing a footnote in Levi-Civita's "The Absolute Tensor Calculus" (1928/1947) p.182: It was first published without proof by Padova (*) 1889 on the strength of a verbal communication by Ricci. Then it was forgotten even by Ricci himself. Bianchi rediscovered it and published a proof in 1902.

(*) E.Padova: "Sulle deformazioni infinitesime: nota", Atti della Reale Accademia dei Lincei, Rendiconti (1889) Serie 4, Volume 5, 1° Semestre, 174-178

See p.176 footnote (1) (via archive.org)

Source Link
Martin Gisser
Martin Gisser
  • 1.1k
  • 2
  • 13
  • 25

1.) The algebraic Bianchi identity must have been known to Riemann, as shown by his posthumously published prize essay to the Paris academy, "Commentatio mathematica ...". Cf. Spivak Vol. II which has an english translation and modern interpretation. (Interesting for German readers: Anmerkungen by Dedekind and Weber in "Bernhard Riemann's gesammelte Mathematische Werke" 1876, 2.Aufl. 1892, p.405ff.)

I haven't checked Delanoe's reference to Christoffel, J. reine angew. Math 70 (1869) 46-70 which should contain the first published proof.

2) The differential Bianchi identity is due to Ricci. Paraphrasing a footnote in Levi-Civita's "The Absolute Tensor Calculus" (1928/1947) p.182: It was first published without proof by Padova 1889 on the strength of a verbal communication by Ricci. Then it was forgotten even by Ricci himself. Bianchi rediscovered it and published a proof in 1902.