Constant Scalar Curvature Sasaki Metrics and Projective Bundles

Abstract

In this paper we consider the Boothby-Wang construction over twist 1 stage 3 Bott orbifolds given in terms of the log pair $(S_{\mathbf{n}},{\Delta }_{\mathbf{m}})$. We give explicit constant scalar curvature (CSC) Sasaki metrics either directly from CSC Kähler orbifold metrics or by using the weighted extremal approach of Apostolov and Calderbank. The Sasaki 7-manifolds (orbifolds) are finitely covered by compact simply connected manifolds (orbifolds) with the rational homology of the 2-fold connected sum of $S^2\times S^5$.

30 pages with 1 table, to appear in the volume: Birational Geometry, Kähler-Einstein Metrics, and Degeneration in the Springer Proceedings in Mathematics & Statistics. The revised version has corrected minor errors and typos, and made clarifications in the introduction