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...
Gespeichert in:
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: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
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 |