# Second Variation of an Action: Part I

So your advisor asks you, “what are the background fluctuations for your action?” If you don’t know what they are talking about, you’ve come to the right place. In the meantime, just smile and wave guys $–$ just smile and wave.

# Integration on Manifolds: Compact Support

Compact support for a metric of a manifold is often required to preform integration on the manifold. However, why is it required? Can one preform integration on a manifold without compact support? We will explore those questions here!