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Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.

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Is any globally-hyperbolic manifold conformally equivalent to one with complete slices?

Let $(M,g)$ be a globally-hyperbolic Lorentzian manifold. By the seminal work of Geroch and Bernal-Sánchez, we know that $$M=\mathbb{R}\times\Sigma,\,\,\,\quad g=-\beta^{2}dt^{2}+h_{t}$$ where $\Sigma …
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