Rigidity under positive Ricci curvature

Establish rigidity results for the compact vacuum static spaces and critical point equation metrics studied in the paper under positive Ricci curvature conditions.

Background

The paper proves rigidity theorems for compact vacuum static spaces and critical point equation metrics under nonnegative or positive sectional curvature, together with a nonnegativity condition on the complete divergence of the Weyl curvature tensor. The authors identify positive Ricci curvature conditions as a setting in which analogous rigidity results have not yet been established. Resolving this issue would extend the paper’s classification results to a broader curvature regime.