differential geometry

[nibot]

Blah. Covariant derivative. Parallel transport. What's the story?

"a geodesic is a curve whose parametrization, when viewed from within the surface, appears to have zero acceleration" (i.e., all of the acceleration is normal to the surface)

The phrase "objects not experiencing external forces follow geodesics" is more of a tautology than I thought.

If gravity is actually a warping of space-time — so that there's not actually any 'force' of gravity, but rather falling objects travel in "straight lines" along geodesics in space time — why is there still the occasional mention of graviton messenger particles for the gravitational force?

sleepy time.

Comments

[calbruin.livejournal.com]

I remember reading about such things in Gravitation (http://www.amazon.com/exec/obidos/tg/detail/-/0716703440/qid=1081793808/sr=1-5/ref=sr_1_5/103-4920087-4747065?v=glance&s=books). I remember it taking me a long time, since I was studying on my own outside of any classroom guidance, to understand what it was describing. In effect, parallel transport is merely "transporting" picking up and moving the vector to another place on a curve. What annoyed me was when I wanted to learn more about "warped" curves, most other texts focused upon the local space-time being flat so that ordinary 1-forms may be applied. I did not care about the baby "flat" region sceniro, I wanted to learn about the hard core problems investigating curved surfaces.