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  "body": "\n## Summary\n\nA space form is a complete connected [[Riemannian manifold|7CBT4SM83Y]] of constant [[sectional curvature|1X42JAA349]].\nThe three simply connected models are the round sphere, Euclidean space and hyperbolic space.\nEvery space form is a quotient of one of these models by a group of isometries.\nSo space forms are the simplest and most symmetric Riemannian manifolds.\nThey serve as the reference spaces in comparison geometry.\n\n## Explanations\n\n### L1 human\n\nA space form is a space that curves by the same amount at every point and in every direction.\nIf the amount is positive, the space looks like a sphere; if it is zero, it looks flat.\nIf it is negative, it looks like the hyperbolic plane, a saddle everywhere.\nA flat torus, made by gluing opposite sides of a square, is a space form of curvature zero.\nAn open disc in the plane is flat but has an edge one can reach in finite distance, so it is not complete and not a space form.\n",
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