Register to reply

Holonomy of compact Ricci-flat Kaehler manifold

by Ygor
Tags: holonomy, kaehler, ricci-flat, su(m)
Share this thread:
Ygor
#1
Jul2-09, 07:27 AM
P: 4
Hi,

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.

Thanks!

Ygor
Phys.Org News Partner Science news on Phys.org
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts

Register to reply

Related Discussions
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