Geodesics in the complement of a Hopf fiber in $S^3$, stereographically projected to $\mathbb{R}^3
This program displays geodesics in the complement of a single fiber of the Hopf fibration of S^3, projected to R^3 via stereographic projection. The Hopf fibration maps the 3-sphere to the 2-sphere, with each fiber being a great circle. The complement of one fiber is topologically a solid torus, and geodesics within it trace out interesting curves when projected to 3-space, illustrating the interplay between the round metric on S^3 and the topology of the fibration.
Controls: Click and drag to orbit, scroll to zoom.
