4 problems

For each $n$, let \mathcal{F}^n = \langle \mathbb{R}^{1+n}, \mathrel{\scalebox{0.85}{oldalpha}} \rangle be the frame of $(1+n)$-dimensional Minkowski spacetime with causal rela…

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 v…

Let $\Sigma$ be a two-dimensional spacelike closed embedded orientable surface in Minkowski spacetime, diffeomorphic to $S^2$. Let $T_0\in\mathbb{R}^{3,1}$ be a fixed future timeli…

Let $\xi_1,\dotsc,\xi_n\subset\mathbb{R}^{3,1}$ be $n$ non-intersecting world lines in Minkowski space, and let $x_i\in\xi_i$ be distinct events. For $i\ne j$, let $u_{ij}$ be the…