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Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics

journal contribution
posted on 25.09.2014, 09:33 by Alexey BolsinovAlexey Bolsinov, Vladimir S. Matveev
Two metrics g and ḡ are geodesically equivalent if they share the same (unparameterized) geodesics. We introduce two constructions that allow one to reduce many natural problems related to geodesically equivalent metrics, such as the classification of local normal forms and the Lie problem (the description of projective vector fields), to the case when the (1, 1)-tensor G := g gkj has one real eigenvalue, or two complex conjugate eigenvalues, and give first applications. As a part of the proof of the main result, we generalise the Topalov-Sinjukov (hierarchy) Theorem for pseudo-Riemannian metrics. © 2011 American Mathematical Society.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transactions of the American Mathematical Society

Volume

363

Issue

8

Pages

4081 - 4107

Citation

BOLSINOV, A.V. and MATVEEV, 2011. Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics. Transactions of the American Mathematical Society, 363 (8), pp.4081-4107.

Publisher

© American Mathematical Society

Version

VoR (Version of Record)

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

2011

Notes

This paper is closed access.

ISSN

0002-9947

Language

en

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