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A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics

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journal contribution
posted on 25.09.2014, 09:21 by Alexey Bolsinov, Volodymyr Kiosak, Vladimir S. Matveev
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.

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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.

Publisher

Oxford Journals (© London Mathematical Society)

Version

SMUR (Submitted Manuscript Under Review)

Publisher statement

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

ISSN

0024-6107

eISSN

1469-7750

Language

en

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