Constant Scalar Curvature Sasaki Metrics and Projective Bundles

TL;DR

This paper constructs explicit constant scalar curvature Sasaki metrics on certain 7-manifolds and orbifolds derived from Bott orbifolds, using both direct and extremal methods, revealing their topological structure.

Contribution

It provides explicit CSC Sasaki metrics on Boothby-Wang constructions over twist stage 3 Bott orbifolds, combining direct and extremal approaches.

Findings

Explicit CSC Sasaki metrics constructed

Manifolds have the rational homology of 2-fold connected sum of S^2×S^5

Sasaki 7-manifolds are finitely covered by simply connected manifolds

Abstract

In this paper we consider the Boothby-Wang construction over twist 1 stage 3 Bott orbifolds given in terms of the log pair $(S_{\bf n},\Delta_{\bf m})$. We give explicit constant scalar curvature (CSC) Sasaki metrics either directly from CSC K\"ahler 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 $S^2\times S^5$.