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Conformally flat manifolds

  1. Dec 30, 2009 #1
    Why all two dimensional manifolds are conformally flat?
    Why all manifolds with constant sectional curvature are conformally flat?
    Does anyone know proofs of above statements.
    Thanks in advance.
  2. jcsd
  3. Jan 6, 2010 #2
    On a surface one can always find coordinates where the metric is a scalar times the standard flat metric on the coordinate tangent vectors. You should try to prove this yourself. It was first proved by Gauss. You will get a PDE.

    For constant sectional curvature I will have to think about it.
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