Can we put a flat metric on any subset of $\mathbb{R}^D$ that's diffeomorphic to an open subset on $\mathbb{R}^d, d < D?$ (just checking!)

Question

Let $V \subset \mathbb{R}^D$ is diffeomorphic to an open subset $U \subset \mathbb{R}^d, d <D.$ Let $\phi: V\to U$ be a diffeomorphism. It seems pretty obvious, but I'm just checking to ensure I didn't miss anything: we can induce a flat metric on $V$ by pulling back the Euclidean metric from $U$ onto $V,$ right? If it's right, then we can easily put a flat metric on $\mathbb{S}^2 -\{(0,0,1)\}, $ am I right?