Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics
نویسندگان
چکیده
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 Gj := g ik ḡkj has one real eigenvalue, or two complex conjugate eigenvalues, and give first applications. As a part of the proof of the main result, we generalize Topalov-Sinjukov (hierarchy) Theorem for pseudo-Riemannian metrics
منابع مشابه
Splitting and Gluing Lemmas for Geodesically Equivalent Pseudo-riemannian Metrics
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 Gj := g ik ḡkj has one r...
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