Greatest Lower Bounds on Ricci Curvature for Fano $T$-manifolds of Complexity $1$

TL;DR

This paper determines the greatest lower bounds on Ricci curvature for all Fano T-manifolds of complexity one, extending previous results and utilizing advanced geometric methods.

Contribution

It generalizes Chi Li's results to a broader class of Fano T-manifolds of complexity one using new geometric techniques.

Findings

Computed the greatest lower bounds on Ricci curvature for all Fano T-manifolds of complexity one.

Extended previous results from simpler cases to more complex manifolds.

Utilized the work of Datar, Székelyhidi, Ilten, and Süss for the proof.

Abstract

In this short note we determine the greatest lower bounds on Ricci curvature for all Fano $T$-manifolds of complexity one, generalizing the result of Chi Li. Our method of proof is based on the work of Datar and Sz\'ekelyhidi, using the description of complexity one special configurations given by Ilten and S\"u\ss.