Fubini Theorem for pseudo-Riemannian metrics

Details Fubini Theorem for pseudo-Riemannian metrics Fubini Theorem for pseudo-Riemannian metrics

2008-06-16

arxiv.org/abs/0806.2632v1

Journal of the London Mathematical Society 80(2009) no. 2, 341--356

Mathematics

Differential Geometry

Scientific paper

We generalize the following classical result of Fubini for pseudo-Riemannian metrics: if three essentially different metrics on $M^{n\ge 3}$ share the same unparametrized geodesics, and two of them (say, $g$ and $\bar g$) are strictly nonproportional (i.e., the minimal polynomial of $g^{i\alpha} \bar g_{\alpha j}$ coincides with the characteristic polynomial) at least at one point, then they have constant curvature.

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