#### Volume 10, issue 4 (2006)

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Highly connected manifolds with positive Ricci curvature

### Charles P Boyer and Krzysztof Galicki

Geometry & Topology 10 (2006) 2219–2235
 arXiv: math.DG/0508189
##### Abstract

We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k–fold connected sum of ${S}^{2n-1}×{S}^{2n}$ admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and 11.

##### Keywords
Sasakian manifold, positive Ricci curvature, links, diffeomorphism type, highly connected
Primary: 53C25
Secondary: 57R55