In the literature are there some concept of geometric version of Morse or Picard Lefschets theory? That is the comparison of level sets as Riemannian submanifold not merely as topological manifolds.

In particular is there a complete classification of Polynomials $P(z,w): \mathbb{C}^2 \to \mathbb{C}$ such that all regular level sets are mutually isometric Riemannian manifolds when we consider them as $2$ dimensional submanifolds of $\mathbb{R}^4 \simeq \mathbb{C}^2$ where level sets inherit the standard metric $dx_1^2+dy_1^2+dx_2^2+dy_2^2$ of $\mathbb{R}^4$? In particular does $z^2+w^2$ satisfy this property? Here we identify $(z,w)\in \mathbb{C}^2$ with $(x_1,y_1,x_2,y_2) \in \mathbb{R}^4$ with $z=x_1+iy_1,\;\;w=x_2+iy_2$.