It's not so much a warping phenomenon of spacetime as it's a wavelike phenomenon that creates an over density in the material within a disk of material. You can get standing waves (which is what occurs in galaxies) or moving waves which occur in substances like fluids (e.g. water). The material within the disks can be moving slower or faster than the waves, but where it encounters the wave it enters those conditions of over density and gets compressed. That's where you get your HII regions and OB associations forming. These generally hang around in the areas of over density because they don't last very long and so you get your spiral arm pattern forming. The rest of the materials within the galaxy rotate at whatever speed they will, depending on their distance from the centre and the other factors affecting their movement, but the wave essentially stays put...the spiral pattern doesn't rotate, or moves very little.
Just notice something cool....play that little video of the spiral arms in the galaxy on the right hand side of the page, then quickly look up at M81....you can see the optical illusion of its arms actually rotating
If you want a really good book about galaxies and about spiral density waves in galaxies, grab yourself a copy of this
Galactic Dynamics (Princeton Series in Astrophysics). It is quite maths heavy but you'll just have to wade through it. It's an exceptionally good book and will explain what you need to know about galaxies.
Oh, and I forgot, this book too....
Galactic Astronomy. Also very good.