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Non-affine Connections

  1. Nov 5, 2014 #1
    "Everyone" knows what an affine connection on a smooth manifold is a.k.a. covariant derivative. My questions are:
    i) Why are those connections called affine?
    ii) Is there a mathematical object that 'connects neighboring tangent spaces', that could be termed a 'non-affine connection'?
  2. jcsd
  3. Nov 5, 2014 #2


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    I quote wikipedia: "The terminology [affine connection] is due to Cartan and has its origins in the identification of tangent spaces in Euclidean space Rn by translation: the idea is that a choice of affine connection makes a manifold look infinitesimally like Euclidean space not just smoothly, but as an affine space."

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