Splitting and gluing lemmas for geodesically equivalent pseudo-riemannian metricsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 26 сентября 2016 г.
Аннотация:Two metrics g and g' 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^j_i := g_{ik}(g')^{kj} 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.