Let f f be an isometric immersion of a Riemannian manifold M M into M ¯ \overline M . We prove that if f f is constant isotropic, 4 4 -planar geodesic and M ¯ \overline M is a Euclidean sphere, then M M is isometric to one of compact symmetric spaces of rank equal to one and f f is congruent to a direct sum of standard minimal immersions. We also determine constant isotropic, 4 4 -planar geodesic, totally real immersions into a complex projective space of constant holomorphic sectional curvature.