# Curvature of hypersurface in flat spacetime

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.

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