What you normally think of as a torus is actually an embedding of the torus in a higher dimensional Euclidean (flat) space. The surface of the torus *as a space of its own* seems flat everywhere to a Flatlander constrained to live within that surface.
What you normally think of as a torus is actually an embedding of the torus in a higher dimensional Euclidean (flat) space. The surface of the torus *as a space of its own* seems flat everywhere to a Flatlander constrained to live within that surface.