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.