2134/15933
Alexey Bolsinov
Alexey
Bolsinov
Vladimir S. Matveev
Vladimir S.
Matveev
Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics
Loughborough University
2014
untagged
Mathematical Sciences not elsewhere classified
2014-09-25 09:33:38
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Splitting_and_gluing_lemmas_for_geodesically_equivalent_pseudo-Riemannian_metrics/9377966
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.