A result on Ricci curvature and the second Betti number

Jianming Wan
2014 Asian Journal of Mathematics  
We prove that the second Betti number of a compact Riemannian manifold vanishes under certain Ricci curved restriction. As consequences we obtain an interesting curved restriction for compact Kähler-Einstein manifolds and a homology sphere theorem in dim = 4, 5.
doi:10.4310/ajm.2014.v18.n4.a2 fatcat:phigqya6irhodhiehw54ms7sfq