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

TL;DR

This paper constructs new families of compact minimal submanifolds of specific classical Riemannian symmetric spaces using complex-valued eigenfunctions, advancing understanding of their geometric structures.

Contribution

It introduces novel multi-dimensional families of minimal submanifolds in these symmetric spaces, expanding the catalog of known minimal submanifold examples.

Findings

New families of minimal submanifolds constructed

Applicable to spaces like $SU(n)/SO(n)$, $Sp(n)/U(n)$, etc.

Submanifolds have codimension two

Abstract

In this work we construct new multi-dimensional families of compact minimal submanifolds, of the classical Riemannian symmetric spaces $SU(n)/SO(n)$, $Sp(n)/U(n)$, $SO(2n)/U(n)$ and $SU(2n)/Sp(n)$, of codimension two.