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Fubini Theorem for pseudo-Riemannian metrics

By Alexey V. Bolsinov, Volodymyr Kiosak and Vladimir S. Matveev

Abstract

We generalize the following classical result of Fubini [12] for pseudo-Riemannian metrics: if three essentially different metrics on M n≥3 share the same unparametrized geodesics, and two of them (say, g and ¯g) are strictly nonproportional (i.e., the minimal polynomial of g iα ¯gαj coincides with the characteristic polynomial) at least at one point, then they have constant curvature.

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.311.3696
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