We generalize the following classical result of Fubini to pseudo-Riemannian metrics: if three essentially different metrics on an (n ≥ 3)-dimensional manifold M share the same unparametrized geodesics, and two of them (say, g and g) are strictly nonproportional (that is, the minimal polynomial of the g-self-adjoint (1, 1)-tensor defined by g coincides with the characteristic polynomial) at least at one point, then they have constant sectional curvature.
History
School
Science
Department
Mathematical Sciences
Published in
Journal of the London Mathematical Society
Volume
80
Issue
2
Pages
341 - 356
Citation
BOLSINOV, A.V., KIOSAK, V. and MATVEEV, V.S., 2009. A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics. Journal of the London Mathematical Society, 80 (2), pp. 341-356.
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
Publication date
2009
Notes
This is the submitted version. The final published version can be found at: http://dx.doi.org/10.1112/jlms/jdp032