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Nov 15, 2012 at 18:42 comment added Pablo Lessa Sorry, I apparently misunderstood your question. Bryant's answer is exactly what I was looking for.
Nov 15, 2012 at 15:33 comment added Paul Reynolds Given that you've accepted Robert Bryant's answer below, I think the answer to my question should actually be no. Unless I've misunderstood completely, your question is answered by the notion of holonomy subbundle.
Nov 15, 2012 at 10:30 comment added Pablo Lessa Yes, although the Riemannian metric chosen on $OM$ doesn't play a role in this question.
Nov 15, 2012 at 10:29 history edited Pablo Lessa CC BY-SA 3.0
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Nov 15, 2012 at 10:27 vote accept Pablo Lessa
Nov 14, 2012 at 19:53 answer added Robert Bryant timeline score: 7
Nov 14, 2012 at 18:37 comment added Paul Reynolds Are you talking about the holonomy group of the total space of $OM$ with its usual (Sasaki-Moek/O'Neill) Riemannian metric?
Nov 14, 2012 at 17:56 history asked Pablo Lessa CC BY-SA 3.0