RT Journal Article
T1 Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank
A1 Domínguez Vázquez, Miguel
A1 Sanmartín López, Víctor
K1 Isoparametric hypersurface
K1 Inhomogeneous
K1 Austere submanifold
K1 Symmetric space
K1 Non-compact type
K1 Hyperpolar
K1 Extension
AB We construct inhomogeneous isoparametric families of hypersurfaces with non-austere focal set on each symmetric space of non-compact type and rank  ≥3. If the rank is  ≥4, there are infinitely many such examples. Our construction yields the first examples of isoparametric families on any Riemannian manifold known to have a non-austere focal set. They can be obtained from a new general extension method of submanifolds from Euclidean spaces to symmetric spaces of non-compact type. This method preserves the mean curvature and isoparametricity, among other geometric properties
PB Cambridge University Press
SN 0010-437X
YR 2024
FD 2024
LK http://hdl.handle.net/10347/33000
UL http://hdl.handle.net/10347/33000
LA eng
NO Domínguez-Vázquez M, Sanmartín-López V. Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank. Compositio Mathematica. 2024;160(2):451-462. doi:10.1112/S0010437X23007650
NO We would like to thank J. Berndt, E. García-Río, J. M. Manzano, H. Tamaru, and the anonymous referees for helpful comments and suggestions. We are grateful to I. Solonenko for pointing out an issue in the study of the congruence in a previous version of this article
DS Minerva
RD 28 abr 2026