Isoparametric hypersurfaces in Damek–Ricci spaces
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Abstract
We construct uncountably many isoparametric families of hypersurfaces in Damek-Ricci spaces. We characterize those of them that have constant principal curvatures by means of the new concept of generalized Kähler angle. It follows that, in general, these examples are inhomogeneous and have nonconstant principal curvatures.
We also find new cohomogeneity one actions on quaternionic hyperbolic spaces, and an isoparametric family of inhomogeneous hypersurfaces with constant principal curvatures in the Cayley hyperbolic plane
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This is the accepted manuscript of the following article: Díaz-Ramos, José Carlos; Domínguez-Vázquez, Miguel; Isoparametric hypersurfaces in Damek-Ricci spaces. Adv. Math. 239 (2013), 1–17. https://doi.org/10.1016/j.aim.2013.02.010
Bibliographic citation
Díaz-Ramos, José Carlos; Domínguez-Vázquez, Miguel; Isoparametric hypersurfaces in Damek-Ricci spaces. Adv. Math. 239 (2013), 1–17
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https://doi.org/10.1016/j.aim.2013.02.010Sponsors
The first author has been supported by a Marie-Curie European Reintegration Grant (PERG04-GA-
2008-239162). The second author has been supported by the FPU programme of the Spanish Government. Both authors have been supported by projects MTM2009-07756 and INCITE09207151PR (Spain)
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© 2013 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (http:// creativecommons.org/licenses/by-nc-nd/4.0/)