Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Exercise [14.08]
Author Message

Joined: 26 Mar 2010, 04:39
Posts: 109
Exercise [14.08]
Recall from the Exercise 14.7 that the torsion tensor is given by:

Writing

we can see immediately that the torsion contribution will only come from the final term and so:

Hence the general expression including torsion is:

Although not required for this question, the curvature tensor can be calculated by simplifying the the first four terms in the previous equation to get:

(I show the details of how to arrive at this result in my response to Exercise 14.27)

04 May 2010, 08:07

Joined: 23 Aug 2010, 13:12
Posts: 33
Re: Exercise [14.08]
I had a lot of trouble with this derivation until I realized that the a and b indices on the left hand side of the second equation (the one following "writing") should be interchanged.

24 Aug 2010, 12:51

Joined: 26 Mar 2010, 04:39
Posts: 109
Re: Exercise [14.08]
Yes - well spotted again. It's really easy to mess things up typesetting all those indices.

25 Aug 2010, 05:06
 Page 1 of 1 [ 3 posts ]