robertson-walker metric

[Ratzinger]

This metric is often written in an alternative form, here (http://en.wikipedia.org/wiki/Friedmann-Lema%C3%AEtre-Robertson-Walker_metric) called the curvature normalized way. Unfortunately I can't follow how they rewrite it, could someone hint me how it is done or tell me a text where it is shown in more detail?

thanks

[Ich]

The derivation is straightforward once you know that sin^{-1} means arcsin there.