Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank

Autor:	Dominguez-Vazquez, Miguel, Sanmartin-Lopez, Victor
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry 53C40 53C35 53C42
Druh dokumentu:	Working Paper
Popis:	We construct inhomogeneous isoparametric families of hypersurfaces with non-austere focal set on each symmetric space of non-compact type and rank greater than or equal to 3. If the rank is greater than or equal to 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. Comment: 13 pages. Minor changes. Accepted for publication in Compositio Mathematica
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.03850 Zobrazit plný text záznamu View this record from Arxiv