Palais-Smale sequences for the prescribed Ricci curvature functional

TL;DR

This paper characterizes divergent Palais-Smale sequences for the prescribed Ricci curvature functional on compact homogeneous spaces, establishing existence of saddle points and describing the Ricci map's image in specific examples.

Contribution

It provides a complete description of divergent Palais-Smale sequences and proves the existence of saddle points on certain homogeneous spaces, advancing understanding of the Ricci curvature functional.

Findings

Complete description of divergent Palais-Smale sequences

Existence of saddle points on generalized Wallach spaces

Description of the Ricci map's image in examples

Abstract

We obtain a complete description of divergent Palais-Smale sequences for the prescribed Ricci curvature functional on compact homogeneous spaces. As an application, we prove the existence of saddle points on generalized Wallach spaces and several types of generalized flag manifolds. We also describe the image of the Ricci map in some of our examples.