Homework Help: Differential coefficients & metric tensor (Urgent)

1. Nov 30, 2011

andrey21

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$\nu$ of I2

As for the differential coefficients would they simply be:

∂f=∂f/∂x . ∂x + ∂f/∂y . ∂y for (x,y)

and

∂f=∂f/∂p . ∂p + ∂f/∂q . ∂q for (p,q)

Any help would be greatly appreciated!