Invariant submanifolds of contact (κ, μ)-manifolds

Invariant submanifolds of contact (kappa, mu)-manifolds are studied. Our main result is that any invariant submanifold of a non-Sasakian contact (kappa, mu)-manifold is always totally geodesic and, conversely, every totally geodesic submanifold of a non-Sasakian contact (kappa, mu)-manifold, mu not equal 0, such that the characteristic vector field is tangent to the submanifold is invariant. Some consequences of these results are then discussed.