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Computing the components of the curvature tensor is tedious, are there other methods?

  1. May 28, 2012 #1
    I've been trying to calculate the Riemann Curvature Tensor for a certain manifold in 3-dimensional Euclidean Space using Christoffel Symbols of the second kind, and so far everything has gone well however...

    It is extremely tedious and takes a very long time; there is also a high probability of making silly mistakes (like misplacing a variable). Are there any faster methods (not necessarily simpler) or is there no other alternative?
     
  2. jcsd
  3. May 28, 2012 #2

    lavinia

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    Re: Computing the components of the curvature tensor is tedious, are there other meth

    The equations simplify with respect to an orthonormal basis.

    For a surface, if dx and dy are a local orthonormal basis for the 1 forms, then

    dx = w[itex]_{12}[/itex]^dy and dy = -w[itex]_{12}[/itex]^dx

    dw[itex]_{12}[/itex] = -KdV where K is the Gauss curvature and dV is the volume element of the metric.
     
    Last edited: May 28, 2012
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