Highly connected manifolds with positive Ricci curvature

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 $S^{2n-1}\times S^{2n}$ 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.