English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We present polyhedral models for isoparametric families in the sphere with at most three principal curvatures. Each member of the family (including the analogues of the focal sets) is tight in the boundary complex of an ambient convex polytope. In particular, the tube around the real (or complex) Veronese surface is represented as a tight polyhedron in 5-space (or 8-space). The examples are based on a certain Bier sphere triangulation of  S  4  or  S  7 , respectively. In the 4-dimensional case there are simplicial branched coverings of these triangulations in the complex projective plane and in  S  2  ×  S  2  which are branched precisely along the polyhedral analogues of the Veronese surface. Moreover, we introduce a notion of PL-tautness and discuss its relationship with tightness of polyhedra. In particular, each member of our polyhedral isoparametric family is PL-taut. For an extended abstract see [W. Kühnel, Discrete models of isoparametric hypersurfaces in spheres.  Oberwolfach Reports  12 , 665–667 (2006).].

Tight polyhedral models of isoparametric families, and PL-taut submanifolds