Relationships among non-flat totally geodesic surfaces in symmetric spaces of type A and their polynomial representations

Abstract

We give computational systems of polynomial representations of the composition maps of non-flat totally geodesic surfaces of the symmetric spaces of type A which are obtained by K. Mashimo, and the Cartan imbeddings of symmetric spaces of type A to $SU(n)$. We obtain the relationships among the non-flat totally geodesic surfaces in symmetric spaces of types AI, AII and AIII by this methods.