Geometric Formality

• Antragsteller: Professor Dieter Kotschick, Ph.D.
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2003 bis 2008
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 5406609

We shall investigate Riemannian metrics on compact oriented manifolds for which all wedge products of harmonic forms are harmonic. In small dimensions, we aim to classify these metrics. In arbitrary dimensions, forms harmonic for such a metric have very special properties and define interesting geometric structures, like foliations and symplectic structures. We investigate homogeneous examples, and those close to homogeneous (e.g. of cohomogeneity one, or biquotients). Further we study constructions of such metrics via symplectic geometry. Within symplectic geometry, we study the analogous property for symplectically harmonic forms in the sense of Brylinski instead of the harmonic forms in the sense of Hodge theory.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1154: Globale Differentialgeometrie