# The Hopf fibration 4

## Universitatea Alexandru Ioan Cuza

We recall some classical results on the Hopf fibration \(f:S^3 \rightarrow S^2\). We focus on the preimage of a curve gamma on \(S^2\) via the projection \(f\). It is known as the Hopf tube over gamma and we give some curvature properties. We point out, as application related to Physics, some developments on magnetic curves on the 3-dimensional sphere. We complete the lectures extending all these studies to the fibration \(M^3(c) \rightarrow S^2(r)\), where \(M^3(c)\) is an elliptic Sasakian space form.