Characterizations of model manifolds by means of certain differential systems

TL;DR

This paper establishes metric rigidity results for complete manifolds supporting solutions to specific second order differential systems, extending classical space-form characterizations and introducing new characterizations of space-forms.

Contribution

It extends classical space-form characterizations by proving metric rigidity for manifolds with solutions to certain differential systems and introduces new characterizations of space-forms.

Findings

Proves metric rigidity for manifolds with solutions to second order differential systems.

Discovers new characterizations of space-forms.

Generalizes metric rigidity results involving vector fields.

Abstract

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations involving vector fields.