Strongly nonnegative curvature

TL;DR

This paper shows that all known manifolds with nonnegative sectional curvature can have their curvature operator adjusted with a 4-form to become positive-semidefinite, revealing a stronger underlying geometric property.

Contribution

It introduces a new condition strengthening nonnegative curvature by modifying the curvature operator with a 4-form, applicable to all known examples.

Findings

All known nonnegatively curved manifolds satisfy the stronger condition.

The curvature operator can be made positive-semidefinite via a 4-form modification.

This condition may lead to new insights into the structure of nonnegatively curved manifolds.

Abstract

We prove that all currently known examples of manifolds with nonnegative sectional curvature satisfy a stronger condition: their curvature operator can be modified with a 4-form to become positive-semidefinite.