Helix surfaces in the Berger sphere

MONTALDO, STEFANO;ONNIS I. I.

2014-01-01

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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