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arXiv · 0806.2632

Fubini Theorem for pseudo-Riemannian metrics

Alexey V. Bolsinov·Volodymyr Kiosak·Vladimir S. Matveev
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Abstract

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 $g^{iα} \bar g_{αj}$ coincides with the characteristic polynomial) at least at one point, then they have constant curvature.

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BibTeXRIS

Alexey V. Bolsinov, Volodymyr Kiosak, Vladimir S. Matveev. 2008-06-16. Fubini Theorem for pseudo-Riemannian metrics. https://arxiv.org/abs/0806.2632

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