A submanidfold S of a Riemannian manifold is called a totally geodesic submanifold if every geodesic of S is also a geodesic of M. Totally geodesic submanifolds of Riemannian symmetric spaces have long been studied by many mathematicians. We give a classification of non-flat totally geodesic surfaces of the Riemannian symmetric space of type AI, AIII and BDI.
Irreducible Representation Riemannian Symmetric Space Geodesic Submanifold Involutive Automorphism Standard Orthonormal Basis
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Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic press, New York (1978)MATHGoogle Scholar