I was asked to give a talk to a mixture of undergraduate and graduate students on a topic of my choosing from differential geometry. The students will mostly not be in geometry; however, I believe I can assume they know the definition of a manifold, vector fields and integral curves as well as differential forms along with some other basic concepts.
I am looking for some suggestions of concepts in geometry, which can be geared towards a not-so-geometrical audience, that are really attention grabbing. The talk will be pretty informal and an hour long.
The talk can be in other areas of geometry too (Riemannian, Sympletic,...) but accessible enough that I can explain what I need to before getting to the crux, or the cool part, of the talk