How can I show that there is no isometry between a sphere and a plane?
Wikipedia defines an isometry as follows:
Let $(M,g)$ and $(M',g')$ be two Riemannian manifolds, and let $f:M\to M'$ be a diffeomorphism. Then $f$ is called an isometry if $g'=f^*g'$, where $f^*g'$ denotes the pullback of the rank $(0,2)$ metric tensor $g'$ by $f$.
However, I have no clue how to apply this definition to solve this problem. Any hint would be greatly appreciated!