Kavli Affiliate: Yi Zhou
| First 5 Authors: Jianquan Ge, Jianquan Ge, , ,
| Summary:
Motivated by Bryant’s research on austere subspaces and Cartan’s
isoparametric hypersurfaces with 3 distinct principal curvatures, we construct
three families of austere submanifolds with flat normal bundle in unit spheres.
From these examples we find three irreducible proper Dupin hypersurfaces with 5
distinct principal curvatures of different multiplicities. Thus, we give a
negative answer to an open question raised by Thorbergsson in 2000 which is
instructive for the local classification of proper Dupin hypersurfaces.
Moreover, as an application, we obtain an upper bound estimate for the
dimension of austere subspaces.
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