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  "body": "\n## Summary\n\nA Cartan connection describes the geometry of a manifold as a curved version of a model homogeneous space $G/H$.\nAt each point the manifold is identified to first order with the model, and the connection says how these identifications fit together.\nIts curvature measures how far the manifold is from being locally the model, and it vanishes exactly when the manifold is locally isomorphic to $G/H$.\nRiemannian, conformal and projective geometry all fit in this frame, with models Euclidean space, the conformal sphere and projective space.\n\n## Explanations\n\n### L1 human\n\nThink of rolling a ball without slipping over a curved surface.\nAt each moment the ball touches the surface at one point, and rolling compares the surface with the ball's round shape.\nA Cartan connection works the same way, with any model space in place of the ball.\nFor a flat plane rolled on itself nothing changes, and the curvature is zero.\nFor a curved surface rolled on the flat plane, going around a loop leaves the plane slightly turned, and this is the curvature.\n",
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