term for distance preserving up to scale

Question

Is there a common/established term for distance preserving up to scale?

E.g. Consider two Riemannian manifolds $M \subset \mathbb{R}^m$ and $N \subset \mathbb{R}^n$ equipped with metrics $g_M$ and $g_N$ inherited from their respective ambient Euclidean spaces, and let
$\mathcal{F}((M,g_M), (N,g_N)) = \{f:M\to N | g_M=f^*g_N\}/\sim$
where $f\sim g$ if there exists some constant $c\in\mathbb{R}$ s.t. $f = cg$.

Is there a name for elements of $\mathcal{F}$?

Answer 1

The correct term is homothetic.