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Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form

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arxiv 2109.03098 v2 pith:6PARHDWS submitted 2021-09-07 math.DG

S. Bandyopadhyay , B. Dacorogna , V.S. Matveev , M. Troyanov This is my paper · ORCID
classification math.DG
keywords necessarybernhardbilinearconditionsflatformgiveriemann
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We generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give explicit necessary and sufficient conditions for a tensor field of type (0,2) which is not necessary symmetric or skew-symmetric, and is possibly degenerate, to have constant entries in a local coordinate system.

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    gr-qc 2025-02 reject novelty 4.0 of 10

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