  In the first part of this paper, we extend the result of Li-Wang on the
linearized embedding problem to a compact manifold of arbitrary dimension.
Using this, we then show that any metric perturbation of a embedded $n$-sphere
is also isometrically embedded up to a solution of the homogenous Codazzi
equation, irrespective of the ambient geometry. In the second part we
specialize to dimension two, and study these results within an ambient Null
Cone. Specifically, given a path of metrics on the 2-sphere and an initial
isometric embedding, we develop a small parameter existence and uniqueness
theorem for paths of isometric embeddings. In the final part, after imposing
asymptotic decay conditions on the Null Cone, we show that any metric on the
2-sphere can be isometrically embedded up to a scaling factor. We then prove
the existence of a foliation in a neighborhood of infinity.
