On the Critical Points of the E_k Functionals in Kahler Geometry

TL;DR

This paper proves that certain critical points of the E_k functional with nonnegative Ricci curvature in Kahler geometry are necessarily Kahler-Einstein, advancing understanding of geometric structures in this field.

Contribution

It establishes that critical points of the E_k functional with nonnegative Ricci curvature are Kahler-Einstein, addressing a question posed by X.X. Chen.

Findings

Critical points of E_k with nonnegative Ricci curvature are Kahler-Einstein.

Provides partial answer to Chen's question on E_k functionals.

Advances understanding of geometric conditions leading to Kahler-Einstein metrics.

Abstract

We prove that a Kahler metric in the anticanonical class which is a critical point of the functional E_k and has nonnegative Ricci curvature, is necessarily Kahler-Einstein. This partially answers a question of X.X.Chen.