Helix surfaces in the Berger Sphere
arXiv:1206.1274
Abstract
We characterize helix surfaces in the Berger sphere, that is surfaces which form a constant angle with the Hopf vector field. In particular, we show that, locally, a helix surface is determined by a suitable 1-parameter family of isometries of the Berger sphere and by a geodesic of a 2-torus in the 3-dimensional sphere.
The main theorem has been modified and improved. Final version to appear in Israel Journal of Mathematics