Here are the homework problems for reference. I will type additional details under them. I'm having a lot of trouble and I'm completely lost.
Diff Geometry problem | Flickr - Photo Sharing!
formula 2(b) mentioned in the link/problem above:
Covariant derivative formula | Flickr - Photo Sharing!
Second problem:
Diff Geom problem 2 | Flickr - Photo Sharing!
My main issue with the first problem is that I get a huge mess that can't possibly be correct whenever I plug in the equations for X and Y, and try to differentiate between i, j, k, etc.
My main issue with the second is that I don't understand how to calculate the covariant derivative (trianglea'(t) of a'(t), as mentioned in 4(a)), nor how to prove that it is geodesic.
Thanks in advance for your help.