Positive intermediate Ricci curvature with maximal symmetry rank

Abstract

Generalizing the foundational work of Grove and Searle, the second author proved upper bounds on the ranks of isometry groups of closed Riemannian manifolds with positive intermediate Ricci curvature and established some topological rigidity results in the case of maximal symmetry rank and positive second intermediate Ricci curvature. Here, we recover even stronger topological rigidity, including results for higher intermediate Ricci curvatures and for manifolds with nontrivial fundamental groups.