Extremal Sasakian Metrics on S^3-bundles over S^2

TL;DR

This paper proves the existence of extremal Sasakian metrics on S^3-bundles over S^2, showing they form a collection of open cones called a bouquet, advancing understanding of geometric structures on these manifolds.

Contribution

It establishes the existence of extremal Sasakian metrics on S^3-bundles over S^2 within a novel framework of open cones called a bouquet.

Findings

Existence of extremal Sasakian metrics on S^3-bundles over S^2

Introduction of the bouquet of open cones for these metrics

Contribution to the geometric analysis of Sasakian structures

Abstract

In this note I prove the existence of extremal Sasakian metrics on S^3-bundles over S^2. These occur in a collection of open cones that I call a bouquet.