Simplicial slices of the space of minimal SU(2)-orbits in spheres

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Let (M3k)SU(2) denote the DoCarmo-Wallach moduli space of SU(2)-equivariant spherical minimal immersions of the three sphere S3 of degree k. Although the complexity of these moduli increases rapidly with k (for example, dim (M3k) SU(2)=O (k2)), we show here that they possess linear slices that are simplices of dimension O(k). The construction of these simplicial slices depend on the DeTurck-Ziller classification of 3-dimensional spherical space forms imbedded into spheres as minimal SU(2)-orbits. The existence of these slices enables us to give asymptotically sharp estimates on a sequence of Grünbaum type measures of symmetry of these moduli.

Original languageEnglish (US)
Pages (from-to)683-699
Number of pages17
JournalBeitrage zur Algebra und Geometrie
Issue number2
StatePublished - Oct 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


  • Eigenmap
  • Moduli
  • Simplex
  • Spherical minimal immersion


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