Talk:Holonomy

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The corrections by User:Serenus suggest a couple of things to me (I'm not an expert in these matters):

(1) Is there a necessary distinction to be made, between holonomy and local holonomy?

(2) Is this topic connected with the Berger list, which is a Requested Article?

Charles Matthews 10:22, 10 May 2004 (UTC)

Answering (2) myself, it seems clear from some Googling that it's 'yes' (for example http://arxiv.org/abs/dg-ga/9508014). But that recent work has shown up some gaps. So, redirecting Berger list here, and adding a note.

Charles Matthews 10:30, 10 May 2004 (UTC)

The illustration of holonomy on the sphere is wrong! The vector field on the left-hand meridian should be perpendicular to the great circle, rather than tangent.

Also, the distinction above should be between holonomy and REDUCED holonomy.

I believe you may be misreading the illustration. The holonomy is at the point A, not the point N (as your post seems to suggest). The "loop" in the diagram is perhaps misleading (since it suggests starting and finishing at N instead of A), and I will do my best to edit the image to move the loop into the correct position when I get the chance. But thanks for catching the mistake above (and in the article). You may have missed a few other instances, and I will fix the remaining cases where it was wrong. silly rabbit (talk) 12:20, 24 March 2008 (UTC)