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arXiv · 1410.6206

A new structural approach to isoparametric hypersurfaces in spheres

Anna Siffert
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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 $\mathbb{R}^{n+2}$. We obtain new geometric insights into classical invariants and identities in terms of the geometry of the Lagrangian submanifold.

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Anna Siffert. 2014-10-22. A new structural approach to isoparametric hypersurfaces in spheres. https://arxiv.org/abs/1410.6206

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