Does a manifold of dimension one has curvature?

Question

Recently I have seen an interesting answer to an "obvious" question. That is "why can we pull a curve back into a line"? And the answer is "because a manifold of dimension one has no curvature". So I was wandering whether that answer is correct or not. Besides, I am not sure why a manifold of dim 1 has no curvature? Looking for someone's answer.

Answer 1

The curves normally have extrinsic curvatures.

For example a circle with radius $R$ has extrinsic curvature of $1/R$.

May be the answer is that curves do not have intrinsic curvature which is another way of saying the intrinsic curvature of a curve is $0$.