Publication

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

Bernard Dacorogna, Marc Troyanov
2023
Journal Articles

Abstract

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

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