Leírás
A hypersurface of a Riemannian manifold is called isoparametric if its nearby parallel hypersurfaces are of constant mean curvature. Classifications of isoparametric hypersurfaces in the Euclidean and hyperbolic spaces are classical results of Segre and Cartan, respectively, however, their classification in the sphere turned out to be a much more difficult problem, completed only in 2016 by Miyaoka using many earlier results of others.
Harmonic manifolds are Riemannian manifolds in which small geodesic spheres are isoparametric hypersurfaces. Damek-Ricci spaces are non-compact harmonic manifolds, including non-compact rank one symmetric spaces and many non-symmetric spaces. As a first step towards a classification of isoparametric hypersurfaces in Damek-Ricci spaces, we construct new families of isoparametric hypersurfaces in these spaces. We also study the geometry of the obtained hypersurfaces.
Joint work with Márton Horváth.
The talk will also be broadcast on Zoom.