Rigidity on non-negative intermediate curvature

TL;DR

This paper investigates the rigidity properties of manifolds with non-negative intermediate curvature in dimensions up to five, extending classical results on scalar curvature and providing new insights into geometric constraints.

Contribution

It extends the study of intermediate curvature rigidity to dimensions up to five, building on recent notions introduced by Brendle-Hirsch-Johne.

Findings

Rigidity results for non-negative intermediate curvature in dimensions ≤5

Extension of classical scalar curvature non-existence theorems

New geometric constraints on product manifolds

Abstract

In a recent work of Brendle-Hirsch-Johne, a notion of intermediate curvature was introduced to extend the classical non-existence theorem of positive scalar curvature on torus to product manifolds. In this work, we study the rigidity when the intermediate curvature is only non-negative when the ambient dimension is at most $5$.