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Can we have a hypersurface in flat spacetime whose curvature is non zero? If yes, then what is the physical significance of that?

I think there can be a hypersurface in flat spacetime with non zero curvature.For example: If hypersurface is $t-vx=constant$ which gives $dt=vdx$ then line element on hypersurface is $ds^2=dt^2-dx^2-dy^2-dz^2=(v^2 -1)dx^2- dy^2- dz^2$ calculating Riemann tensor we can find they are non zero.

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    $\begingroup$ well you can have curved hypersurface in 3D space, why would be spacetime different? $\endgroup$
    – Umaxo
    Sep 16, 2020 at 12:41
  • $\begingroup$ Ahh got it. Thanks. The question seems silly to me now. $\endgroup$ Sep 16, 2020 at 12:50

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