CIRM – Research in Pairs — Nijenhuis Geometry

Nijenhuis operators are defined to be fields of endomorphisms with vanishing Nijenhuis torsion. They appeared as independent objects and play an essential role in different branches of geometry and mathematical physics. The current state of art in this theory is as follows: The definition is well known, basic properties are understood and local normal forms are classified in certain particular cases. Our main goal is to initiate the study of Nijenhuis operators from a global viewpoint. We also aim at understanding their singularities.