Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
Bandyopadhyay, S.; Dacorogna, B.; Matveev, V. S.; Troyanov, M
2023

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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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Title Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
Author(s) Bandyopadhyay, S. ; Dacorogna, B. ; Matveev, V. S. ; Troyanov, M
Published in Mathematische Zeitschrift
Volume 305
Issue 1
Pages 12
Date 2023-09-01
Publisher Springer Heidelberg, Heidelberg
ISSN 0025-5874
1432-1823
Keywords
DOI https://doi.org/10.1007/s00209-023-03335-1
Other identifier(s) View record in Web of Science
Laboratories CAA
Record Appears in Scientific production and competences > SB - School of Basic Sciences > SB Archives > CAA - Chair of Mathematical Analysis and Applications
Scientific production and competences > SB - School of Basic Sciences > Mathematics
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Grant The research of S. Bandyopadhyay is supported by the MATRICS research project grant (File No. MTR/2017/000414): MTR/2017/000414
MATRICS research project grant: MA 2565/6
Swiss SNF
DFG: DP210100951
ARC Discovery Programme
Record creation date 2024-02-23

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