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

DOI10.1007/s00209-023-03335-1zbMath1528.53036arXiv2109.03098MaRDI QIDQ6063908

Marc Troyanov, Saugata Bandyopadhyay, Bernard Dacorogna, Vladimir S. Matveev

Publication date: 8 November 2023

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.03098

zbMATH Keywords

Poisson structurecurvaturesymplectic structureDarboux theoremHamiltonian vector fieldsPfaffian systemsHartman theoremflat coordinatesdegenerate metrics

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Local Riemannian geometry (53B20) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

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• The pullback equation for differential forms
• On the pullback equation \(\varphi ^*(g)=f\)
• On the hypotheses which lie at the bases of geometry. Edited, commented and translated by Jürgen Jost
• The pullback equation for degenerate forms
• Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity
• A geometric proof of Bieberbach's theorems on crystallographic groups
• On isometric immersions of a Riemannian space under weak regularity assumptions.
• Integrable systems and closed one forms
• On fibering certain foliated manifolds over \(S^1\)
• On the smoothness of isometries
• The Myers-Steenrod theorem for Finsler manifolds of low regularity
• On Hölder continuous Riemannian and Finsler metrics
• ON THE RECOVERY OF A MANIFOLD WITH PRESCRIBED METRIC TENSOR
• SYMPLECTIC CONNECTIONS
• A Theorem on Holonomy

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