Complete minimal submanifolds of the non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(2n)/U(n), SU*(2n)/Sp(n) via complex-valued eigenfunctions

TL;DR

This paper constructs new families of complete minimal submanifolds of codimension two in several classical non-compact Riemannian symmetric spaces using complex-valued eigenfunctions.

Contribution

It introduces explicit constructions of minimal submanifolds in these symmetric spaces, expanding the known examples and understanding of their geometry.

Findings

New multidimensional families of minimal submanifolds are constructed.

The submanifolds are of codimension two in the specified symmetric spaces.

The construction utilizes complex-valued eigenfunctions.

Abstract

In this work we construct new multidimensional families of complete minimal submanifolds, of the classical non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(2n)/U(n) and SU*(2n)/Sp(n), of codimension two.