There was research article that showed that gravitational waves and electromagnetic waves loosing energy by the inverse square law. The researchers concluded that, since gravitational waves obey the inverse square law, extra-dimensions don't exist.
Since gravity is the intrinsic curvature, why would the curvature of a submanifold affect the curvature of the extra dimensions. For example, a sphere embedded in a euclidean space. The sphere is curved, yet the space around it is flat.