Sasakian geometry, homotopy spheres and positive Ricci curvature

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homot...

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Bibliographic Details
Published in:Topology (Oxford) 2003-09, Vol.42 (5), p.981-1002
Main Authors: Boyer, Charles P., Galicki, Krzysztof, Nakamaye, Michael
Format: Article
Language:English
Subjects:
Exotic Spheres
Ricci curvature
Sasakian geometry
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Summary:We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ 2 n+1 the moduli space of Sasakian structures has infinitely many positive components determined by inequivalent underlying contact structures. We also prove the existence of Sasakian metrics with positive Ricci curvature on each of the known 2 2 m distinct diffeomorphism types of homotopy real projective spaces RP 4m+1 .
ISSN:0040-9383
1879-3215
DOI:10.1016/S0040-9383(02)00027-7