Recent content by C0nstantine

Thank you for the suggestion!

It's not a "general" theorem I'm working on, it's actually a derivation of the FLRW metric. So, you have a lot of additional stuff simplifying the manifold structure. There's the assumption that ##\Sigma_\tau## is the set of points ##p\in M## such ##t(p) = \tau##, and ##u = \partial / \partial...

I did a calculation and it yields ##\mathcal{L}_u g\rvert_\tau = f(\tau) g\rvert_\tau## where ##g\rvert_\tau## is the metric of ##\Sigma_\tau##. I think that concludes the proof.

Thank you both for your quick answers. Well, the problem I've come up with is that I have a semi-Riemannian manifold ##(M,g)## equipped with a unit vector field ##u## that satisfies the Frobenius integrability condition. The orthogonal hypersurfaces ##\{\Sigma_t\}## are of constant curvature...

Every two semi-Riemannian manifolds of the same dimension, index and constant curvature are locally isometric. If they are also diffeomorphic, are they also isometric?