# Can there be a closed geodesic on surface embedded in R3 with zero Gaussian curvature

I was asked this in differential geometry class and it.is bugging me as i do not know the answer I know a surface of constant Gaussian curvature zero is locally isometric to a plane on which no geodesic is closed as they are lines but the fact that it is a local isometry puzzles me Does someone have an example of a surface with zero Gaussian curvature and a closed geodesic on it? Thanks all

The flat torus doesn't embed smoothly into $\mathbb R^3$, but it does in $\mathbb R^4$.