Complete Minimal Submanifolds of the Non-Compact Duals to the Classical Compact Lie Groups

2026/08/04 by Thomas Jack Munn
Mathematics · #math.DG #msc:53C35 #msc:53C43 #msc:58E20

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arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

We construct new families of complete minimal submanifolds of codimension two in the non-compact duals to the classical compact Lie groups \SOC n/\SO n, \SLC n/\SU n and \SpC n/\Sp n.

Citations

• Compact minimal submanifolds of the Riemannian symmetric spaces SU(n)/SO(n), Sp(n)/U(n), SO(2n)/U(n), SU(2n)/Sp(n) via complex-valued eigenfunctions
• Global eigenfamilies on closed manifolds
• Polynomial harmonic morphisms and eigenfamilies on spheres
• Minimal Submanifolds via Complex-Valued Eigenfunctions
• Explicit proper p-harmonic functions on the Riemannian symmetric spaces SU(n)/SO(n), Sp(n)/U(n), SO(2n)/U(n), SU(2n)/Sp(n)
• Explicit harmonic morphisms and p-harmonic functions from the complex and quaternionic Grassmannians
• Proper r-harmonic functions from Riemannian manifolds
• Harmonic morphisms from the classical compact semisimple Lie groups
• Harmonic morphisms from the Grassmannians and their non-compact duals
• Harmonic Mappings of Riemannian Manifolds