I am trying to think through the following problem, but I'm totally at a loss and can't imagine a surface that would be a valid example. The question is,
"Give an example and a proof to show: Local isometries can shrink but not increase intrinsic distance."
The given definition of local isometry is:
A local isometry F: M-->N of surfaces is a mapping that preserves dot products of tangent vectors (that is, F does).*
Here F* is the derivative map of F.
Any ideas? I really really struggle with this material, so if you could offer anything it would be so helpful!