General helices in the three-dimensional Lorentzian space forms

DOI10.1216/rmjm/1020171565zbMath0985.53009OpenAlexW2000339009WikidataQ125630688 ScholiaQ125630688MaRDI QIDQ5948857

Manuel Barros, Angel Ferrández, Pascual Lucas, Miguel Angel Meroño

Publication date: 12 November 2001

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol31-2/CONT31-2/CONT31-2.html

zbMATH Keywords

Killing fieldsde Sitter space formsgeneral helixLorentzian space formsolving natural equations problemtangent indicatrix

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Curves in Euclidean and related spaces (53A04) Non-Euclidean differential geometry (53A35)

Related Items

Hypersurface constrained elasticae in Lorentzian space forms ⋮ Triharmonic Curves in Heisenberg Group ⋮ Darboux helices in three dimensional Lie groups ⋮ Contributions to differential geometry of isotropic curves in the complex space \(\mathbb{C}^3\). II. ⋮ General helices with timelike slope axis in Minkowski 3-space ⋮ Differential geometry of magnetic and Killing magnetic trajectories in de Sitter 3-space ⋮ Geometrical Aspects of Motion of Charged Particles in Magnetic and Killing Magnetic Fields and Their Corresponding Trajectories in Anti-De Sitter 3-Space ⋮ Unnamed Item ⋮ Polynomial helices in the n-dimensional semi-Euclidean space with index two ⋮ Associated curves of a Frenet curve in the dual Lorentzian space ⋮ Helix surfaces and slant helices in the three-dimensional anti-de Sitter space ⋮ Unnamed Item ⋮ Magnetic trajectories on lightlike surfaces ⋮ Magnetic spherical indicatricies in Minkowski 3-space ⋮ Spacelike helices in Minkowski 4-space \(E_{1}^{4}\) ⋮ Mappings that preserve helices in the n-dimensional Minkowski spaces ⋮ Some associated curves of Frenet non-lightlike curves in \(\mathbb E_{1}^{3}\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Relativistic particles and the geometry of 4-D null curves ⋮ A variational characterization and geometric integration for Bertrand curves ⋮ Spacelike zero mean curvature surfaces in \({\mathbb{L}}^4\) ⋮ Null Cartan curve variations in 3D semi-Riemannian manifold ⋮ Slant helices: a new approximation ⋮ NULL HELICES IN LORENTZIAN SPACE FORMS ⋮ General helices with spacelike slope axis in Minkowski 3-space ⋮ New results for general helix in Euclidean 3-space ⋮ Some integral curves with a new frame ⋮ Pseudo null curve variations for Bishop frame in 3D semi-Riemannian manifold ⋮ General helices with lightlike slope axis ⋮ Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds ⋮ Mappings that transform helices from Euclidean space to Minkowski space ⋮ Slant curves in the Lorentzian warped product manifold \(-I \times_f{\mathbb{E}}^2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On surfaces in the 3-dimensional Lorentz-Minkowski space
• The total squared curvature of closed curves
• Poisson geometry of the filament equation
• 2-type surfaces in \(S_ 1^ 3\) and \(H_ 1^ 3\)
• Codimension One Isometric Immersions Between Lorentz Spaces
• Local geometric invariants of integrable evolution equations
• General helices and a theorem of Lancret