Sasakian geometry, homotopy spheres and positive Ricci curvature.

DOI10.1016/S0040-9383(02)00027-7zbMATH Open1066.53089arXivmath/0201147OpenAlexW2023415911MaRDI QIDQ1401000

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Publication date: 17 August 2003

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Abstract: 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 $scriptstyleSigm{a}^{2n+1}$ 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 $scriptstyle{2}^{2m}$ distinct diffeomorphism types of homotopy real projective spaces in dimension $4m+1$.

Full work available at URL: https://arxiv.org/abs/math/0201147

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