A player races through a manifold, seeking the shortest path. Unlike most racing games, speed does not matter. Animation could depict where other past racers were for your current distance.
Perhaps race through a tube of varying curvature and width. The racecar travels "in a straight line" if given no input, though that might be a tricky concept on curved manifolds.
Even finding the shortest path between two points on the surface of a cube is nontrivial.
Perhaps different skill classes for corresponding to the minimum speed permitted. Higher minimum speed is harder.
2D and 3D manifolds.
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