Helix surfaces for Berger-like metrics on the anti-de Sitter space

Abstract

We consider the Anti-de Sitter space ${\mathbb{H}}_1^3$ equipped with Berger-like metrics, that deform the standard metric of ${\mathbb{H}}_1^3$ in the direction of the hyperbolic Hopf vector field. Helix surfaces are the ones forming a constant angle with such vector field. After proving that these surfaces have (any) constant Gaussian curvature, we achieve their explicit local description in terms of a one-parameter family of isometries of the space and some suitable curves. These curves turn out to be general helices, which meet at a constant angle the fibers of the hyperbolic Hopf fibration.

26 pages. arXiv admin note: text overlap with arXiv:1307.0215