Asian Journal of Mathematics
Volume 18 (2014)
A result on Ricci curvature and the second Betti number
Pages: 603 – 608
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 $\dim = 4,5$.
Ricci curvature, Betti number
2010 Mathematics Subject Classification
Primary 53C20. Secondary 53C25.