Assume that $M$  is  a surface in $\mathbb{R}^{3}$. We denote   its  shape operator by $S$. A  vector field $X$ is  shape related to $Y$ if $S(X)=Y$.
(of course it is not an equivalent relation).

Assume that $X, Y$  are two vector fields on $S^{2}$ with the same singular points. Is there a surface $M$, diffeomorphic to $S^{2}$ via  a  diffeomorphism $\phi: M \to S^{2}$, such that $\phi^{*} (X)$ is shape related to $\phi^{*}(Y)$.