Is there a polynomial function $P: \mathbb{R}^3 \to \mathbb{R}$ with the following property?:

P does not have any critical value and for all $c \neq c'$, $f^{-1}(c)$ and $f^{-1}(c')$ are non isometric Riemannian manifolds(with the metric they inherit from the standard metric of $\mathbb{R}^3$