|Jul2-09, 07:27 AM||#1|
Holonomy of compact Ricci-flat Kaehler manifold
I have come across the following apparent contradiction in the literature. In "Joyce D.D., Compact manifolds with special holonomy" I find on page 125 the claim that if M is a compact Ricci-flat Kaehler manifold, then the global holonomy group of M is contained in SU(m) if and only if the canonical bundle of M is trivial.
In "Candelas, Lectures on Complex manifolds" however, on page 61 I read that any Ricci-flat Kaehler manifold has global holonomy in SU(m) and there is no mentioning of any condition on the the canonical bundle.
Note that I am assuming M to be multiply connected and I am talking about the global holonomy group, i.e. not the restricted holonomy group.
So my questions is, what is going on ? Who is right? (Both somehow provide proofs of their claims).
I hope anyone can help me out.
|holonomy, kaehler, ricci-flat, su(m)|
|Similar Threads for: Holonomy of compact Ricci-flat Kaehler manifold|
|Yau's result for the Ricci curvature on Kahler manifold||Special & General Relativity||5|
|Real~~ How to show a compact set in Euclidean is also compact in another metic||Calculus & Beyond Homework||0|
|PROVING INTERSECTION OF Any number of COMPACT SETS is COMPACT?||Calculus||4|
|Ricci-Tensor from Riemann in higher dimensional flat space||Differential Geometry||4|
|compact-valued range doesnot imply compact graph||Calculus||3|