Fubini Theorem for pseudo-Riemannian metrics

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.

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