Local normal forms for geodesically equivalent pseudo-Riemannian metrics

Bolsinov, Alexey; Matveev, Vladimir

doi:10.1090/S0002-9947-2014-06416-7

Local normal forms for geodesically equivalent pseudo-Riemannian metrics
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by Alexey V. Bolsinov and Vladimir S. Matveev PDF

Trans. Amer. Math. Soc. 367 (2015), 6719-6749 Request permission

Abstract:

Two pseudo-Riemannian metrics $g$ and $\bar g$ are geodesically equivalent if they share the same (unparameterized) geodesics. We give a complete local description of such metrics which solves the natural generalisation of the Beltrami problem for pseudo-Riemannian metrics.

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