Classification of isoparametric hypersurfaces

• Antragsteller: Professor Dr. Linus Kramer
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2003 bis 2010
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 5407075

Isoparametric hypersurfaces are hypersurfaces in spheres with constant principal curvatures. The known examples either come from isotropy representations of symmetric spaces or from representations of Clifford algebras. The isoparametric hypersurfaces arising from symmetric spaces are the principal orbits of the isotropy representation of the symmetric space. In contrast to this, most of the examples arising from Clifford algebras do not admit a transitive isometry group. The classification of isoparametric hypersurfaces is one of the major open problems in submanifold geometry. One aim of the project is the classification of isoparametric hypersurfaces with four distinct principal curvatures. Closely connected to isoparametric submanifolds are manifolds which have the same rational cohomology as a projective space: The diffeomorphism classification of such manifolds is an open problem; in particular, the classification of manifolds which are like projective planes is open. We plan to achieve such a classification.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1154: Globale Differentialgeometrie
• Internationaler Bezug: USA
• Beteiligte Personen: Dr. Stefan Immervoll; Professor Dr. Stephan A. Stolz