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

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

Mathematische Zeitschrift (2023) 305:12 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...

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Bibliographic Details
Main Authors: Bandyopadhyay, S, Dacorogna, B, Matveev, V. S, Troyanov, M
Format: Journal Article
Language:English
Published: 24-07-2023
Subjects:
Mathematics - Differential Geometry
Online Access:Get full text
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Summary:Mathematische Zeitschrift (2023) 305:12 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.
DOI:10.48550/arxiv.2109.03098