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Homework Help: Differential coefficients & metric tensor (Urgent)

  1. Nov 30, 2011 #1
    Consider a flat 2-dimensional plane. This can be described by standard Cartesian coordinates (x,y). We establish a oblique set of axes labelled p and q. p coincides with x but q is at an angle θ to the x-axis.

    At any point A has unambiguous co-ordinates (x,y) in the Cartesian system. In the (p,q) system we can measure the axes either perpendicular or parallel to the axes.

    For the perpendicular system find a relationship between (x,y) and (p,q). Establish differential coefficients and metric tensor.

    The attempt at a solution

    Now I have read that any flat 2 dimensional plane has a metric tensor gμ[itex]\nu[/itex] of I2

    As for the differential coefficients would they simply be:

    ∂f=∂f/∂x . ∂x + ∂f/∂y . ∂y for (x,y)


    ∂f=∂f/∂p . ∂p + ∂f/∂q . ∂q for (p,q)

    Any help would be greatly appreciated!
  2. jcsd
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