Let $(M, g)$ be a complete, noncompact Riemannian $n$-dimensional manifold and let $\phi \colon M \to \mathbb S^n$ be an harmonic map, where $\mathbb S^n$ is the euclidean $n$-dimensional sphere.

What can we say about the image of $\phi$? Of course in general is not an open subset (constant maps are harmonic). But is it at least an open subset of a submanifold of $\mathbb{S}^n$?

Is there a book with a gentle introduction to harmonic maps, harmonic map flow, and their basic properties?

Any help will be highly apreciated!