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

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.

27 pages

Cited by in corpus (4)

• Analyzing Deflection Angles and Photon Sphere Dynamics of Magnetically Charged Black Holes in Nonlinear Electrodynamic
• Orthogonal separation of variables for spaces of constant curvature
• Nijenhuis geometry of parallel tensors
• Parallel differential forms of codegree two, and three-forms in dimension six