クラインの壺
If formula_10 is a smooth two-dimensional connected complete flat Riemannian manifold, then formula_11 must be diffeomorphic to formula_12 formula_13 formula_14 the Möbius strip, or the Klein bottle. Note that the only compact possibilities are formula_15 and the Klein bottle, while the only orientable possibilities are formula_12 formula_17 and formula_18