Positively curved manifolds with maximal symmetry rank

TL;DR

This paper characterizes the smooth closed manifolds that can support positively curved metrics with the highest possible symmetry rank, providing a complete classification based on symmetry considerations.

Contribution

It precisely identifies the smooth closed manifolds admitting positively curved metrics with maximal symmetry rank, advancing the understanding of symmetry in positively curved geometry.

Findings

Complete classification of manifolds with maximal symmetry rank in positive curvature

Identification of geometric constraints for such manifolds

Clarification of the relationship between curvature and symmetry

Abstract

The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.