Is a geodesic always a rectifiable curve?

Question

I am not an expert in differential geometry, but I need to know the following

If any geodesic that joins two points in a compact and Riemannian manifold is necessary a rectifiable curve, or there exists a counterexample that invalidates that affirmation.

Thanks in advance.

Answer 1

A geodesic the solution of some differential equation and therefore it is always smooth.