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Math Help - Finding the curvature of a distorted manifold

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    Finding the curvature of a distorted manifold

    Hi,
    I have a distorted 2D manifold, with Cartesian coordinate system (u,v).
    This has an automorphism with an undistorted manifold with Cartesian coordinates (x,y).

    The automorphism is defined by a vector field (delta_x(x,y), delta_y(x,y)), where delta_x gives the displacement values (u - x) over the manifold, and similarly delta_y the displacement values (v - y).

    My question is how do I find a scalar field F1(u,v), representing the curvature of the distorted manifold with respect to the x displacements given by delta_x(x,y).

    As I recall the curvature of a scalar field is normally given by the Ricci Scalar; but that's too difficult to calculate, so I need a simpler way of determining the distortion at any given point. (It can be an approximate measure; it doesn't have to be precise.)
    Last edited by alexh110; January 4th 2009 at 12:28 PM.
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