Asian Journal of Mathematics

Volume 18 (2014)

Number 4

A result on Ricci curvature and the second Betti number

Pages: 603 – 608



Jianming Wan (Department of Mathematics, Northwest University, Xi’an, China)


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.

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