Positive intermediate Ricci curvature with maximal symmetry rank

TL;DR

This paper extends the understanding of manifolds with positive intermediate Ricci curvature by establishing stronger topological rigidity results, especially for higher intermediate Ricci curvatures and nontrivial fundamental groups, building on and generalizing previous work.

Contribution

It provides new topological rigidity results for manifolds with positive intermediate Ricci curvature, including cases with higher curvatures and nontrivial fundamental groups.

Findings

Stronger topological rigidity results established.

Extensions to higher intermediate Ricci curvatures.

Results applicable to manifolds with nontrivial fundamental groups.

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.