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

We consider the Anti-de Sitter space H 1 3 equipped with Berger-like metrics, that deform the standard metric of 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) const...

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Veröffentlicht in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024-04, Vol.118 (2), Article 54
Hauptverfasser: Calvaruso, Giovanni, Onnis, Irene I., Pellegrino, Lorenzo, Uccheddu, Daria
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Sprache:eng
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Zusammenfassung:We consider the Anti-de Sitter space H 1 3 equipped with Berger-like metrics, that deform the standard metric of 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.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-024-01550-x