- #1

- 135

- 4

1. Under a conformal transformation the metric changes by:

g' -> Ω

^{2}g

2. Under a Weyl transformation the metric changes by:

g' -> exp(-2f)g

3. Any 2D Riemann manifold is locally conformally flat and the metric can be defined in terms of isothermal coordinates.

g = exp(f)(du

^{2}+ dv

^{2})

Where u and v are Euclidean.

How are these all tied together? There appears to be a commonality in form but the multiplying functions are different. Where does the exponential come from?