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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 S2n1 × S2n 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