The hyperplane conjecture for time flat surfaces in Minkowski spacetime

Let $\Sigma$ be a closed surface in $\mathbb{R}^{3,1}$ that is contained in a complete, spacelike hypersurface. A surface is time flat when its associated connection one-form has vanishing divergence, as defined in the paper. Hyperplane conjecture. If $\Sigma$ is time flat, then $\Sigma$ is contained in a spacelike hyperplane. The conjecture is proposed to justify the terminology “time flat” by asserting that such surfaces in Minkowski spacetime have no timelike oscillations; the source does not provide a resolution.