Highly connected manifolds with positive Ricci curvature

Boyer, Charles P; Galicki, Krzysztof

doi:10.2140/gt.2006.10.2219

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Highly connected manifolds with positive Ricci curvature

Charles P Boyer and Krzysztof Galicki

Geometry & Topology 10 (2006) 2219–2235

DOI: 10.2140/gt.2006.10.2219

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

Mathematical Subject Classification 2000

Primary: 53C25

Secondary: 57R55

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Publication

Received: 5 September 2005

Revised: 22 October 2006

Accepted: 13 October 2006

Published: 29 November 2006

Proposed: Gang Tian

Seconded: Leonid Polterovich, Tobias Colding

Authors

Charles P Boyer
Department of Mathematics and Statistics University of New Mexico Albuquerque, NM 87131 USA

Krzysztof Galicki
Department of Mathematics and Statistics University of New Mexico Albuquerque, NM 87131 USA

Volume 10, issue 4 (2006)