Classification of totally real and totally geodesic submanifolds of compact 3-symmetric spaces

Abstract

It is known that each 3-symmetric space admits an invariant almost complex structure $J$, so-called a canonical almost complex structure. By making use of simple graded Lie algebras and an affine Lie algebra, we classify half dimensional, totally real (with respect to $J$) and totally geodesic submanifolds of compact 3-symmetric spaces.