fubiniLMS.pdf (189.68 kB)
A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics
journal contribution
posted on 2014-09-25, 09:21 authored by Alexey BolsinovAlexey Bolsinov, Volodymyr Kiosak, Vladimir S. MatveevWe 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 SocietyVolume
80Issue
2Pages
341 - 356Citation
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
2009Notes
This is the submitted version. The final published version can be found at: http://dx.doi.org/10.1112/jlms/jdp032ISSN
0024-6107eISSN
1469-7750Publisher version
Language
- en