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Title: Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics
Authors: Bolsinov, Alexey V.
Matveev, Vladimir S.
Issue Date: 2011
Publisher: © American Mathematical Society
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.
Abstract: 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.
Description: This paper is closed access.
Version: Published
DOI: 10.1090/S0002-9947-2011-05187-1
URI: https://dspace.lboro.ac.uk/2134/15933
Publisher Link: http://dx.doi.org/10.1090/S0002-9947-2011-05187-1
ISSN: 0002-9947
Appears in Collections:Closed Access (Maths)

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