Jul2-09, 08:36 AM
I have the following question. In "Joyce D.D. Compact manifolds with special holonomy" I read on page 125 that a compact Kaehler manifold with global holonomy group equal to SU(m), has vanishing first betti number, or more specifically vanishing Hodge numbers h^(1,0)= h^(0,1) = 0. However, in "Candelas, Lectures on complex manifolds" the constrains h^1 = 0 is not automatic if the holonomy equals SU(m).
So, I wonder, which case is the correct one?
I hope anyone could help me out,
|Register to reply|
|Holonomy of compact Ricci-flat Kaehler manifold||Differential Geometry||0|
|Betti number||Differential Geometry||10|
|betti numbers and euler characterstic?||General Math||1|
|Holonomy, SO(6), SU(3) and SU(4)||Differential Geometry||2|
|Another vanishing||General Discussion||25|