Real Hypersurfaces in Quaternionic Space Forms Satyisfying Axioms of Planes

A Riemannian manifold satisfies the axiom of 2-planes if at each point, there are suficiently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several definitions of axiom of planes arise naturally when we consider such families of tangent planes. We are able to classify real hypersurfaces in quaternionic space forms satisfying these definitions.