Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifolds

TL;DR

This paper calculates the maximum possible lower bounds on the transverse Ricci curvature for certain compact toric Sasaki manifolds, extending previous work on related geometric structures.

Contribution

It provides explicit bounds for transverse Ricci curvature on specific toric Sasaki manifolds, building on prior foundational results in the field.

Findings

Determined greatest lower bounds for transverse Ricci curvature.

Extended techniques from toric Fano manifolds to Sasaki manifolds.

Connected curvature bounds to topological and geometric properties.

Abstract

We determine the greatest lower bounds on the transverse Ricci curvature of compact toric Sasaki manifolds with positive basic first Chern class and with the first Chern class of the contact bundle being trivial. This is based on Wang-Zhu's and Futaki-Ono-Wang's works, and is an analogue of C. Li's work on toric Fano manifolds.