A new structural approach to isoparametric hypersurfaces in spheres

2014/10/22 by Siffert, Anna · 1 citation
#53C30 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C40 #Secondary 53C55

paper · doi:10.48550/arxiv.1410.6206

Abstract

The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working with the isoparametric hypersurface family in the sphere, we consider the associated Lagrangian submanifold of the real Grassmannian of oriented 2-planes in ℝⁿ⁺². We obtain new geometric insights into classical invariants and identities in terms of the geometry of the Lagrangian submanifold.

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