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Exercise [14.08] http://www.roadtoreality.info/viewtopic.php?f=19&t=1497 
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Author:  robin [ 04 May 2010, 08:07 ] 
Post subject:  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) 
Author:  Smith [ 24 Aug 2010, 12:51 ] 
Post subject:  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. 
Author:  robin [ 25 Aug 2010, 05:06 ] 
Post subject:  Re: Exercise [14.08] 
Yes  well spotted again. It's really easy to mess things up typesetting all those indices. 
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