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In this paper, we study some parameters which determine the relative position of a pair of quaternionic subspaces and a pair of totally geodesic submanifolds in the real hyperbolic space. We extend some results about principal angles between two real and complex subspaces for quaternionic subspaces. We also prove that the distance and the principal angles of certain tangent spaces determine the congruence class of a non-asymptotic pair of totally geodesic submanifolds of the real hyperbolic space under the action of its isometry group.

Principal angles and pairs of totally geodesic submanifolds of the real hyperbolic space