Why is the exponential map clearly the identity map for $\mathbb R^n$?

306 Views Asked by At

Suppose that $M$ is a smooth Riemannian manifold, $q\in M$. There exists an $\epsilon$ such that $\exp_q:B_{\epsilon}(0)\rightarrow M$ is a diffeomorphism. In DoCarmo’s Riemannian Geometry book, it has been written that for $M=\mathbb R^n$, this map $\exp_q$ is the identity map, while $\exp_q(v)=q+v$. So what does DoCarmo mean?