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arXiv · 2301.07400

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

Giovanni Calvaruso·Irene I. Onnis·Lorenzo Pellegrino·Daria Uccheddu
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Abstract

We consider the Anti-de Sitter space $\mathbb{H}^3_1$ equipped with Berger-like metrics, that deform the standard metric of $\mathbb{H}^3_1$ 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.

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Giovanni Calvaruso, Irene I. Onnis, Lorenzo Pellegrino, Daria Uccheddu. 2023-01-18. Helix surfaces for Berger-like metrics on the anti-de Sitter space. https://arxiv.org/abs/2301.07400

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