ON THE GEOMETRY OF THE SPACE OF ORIENTED LINES OF THE HYPERBOLIC SPACE

DOI10.1017/S0017089507003710zbMath1130.53013arXivmath/0702365MaRDI QIDQ5757161

Marcos Salvai

Publication date: 6 September 2007

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702365

zbMATH Keywords

isometry groupsectional curvaturehyperbolic spacealmost complex structurepseudo-Riemannian metrics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Differential geometry of symmetric spaces (53C35) Geodesic flows in symplectic geometry and contact geometry (53D25) Differential line geometry (53A25) Differential invariants (local theory), geometric objects (53A55) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

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Calibrated geodesic foliations of hyperbolic space ⋮ Infinitesimally helicoidal motions with fixed pitch of oriented geodesics of a space form ⋮ The causal topology of neutral 4-manifolds with null boundary ⋮ The magnetic flow on the manifold of oriented geodesics of a three dimensional space form ⋮ A characterization of Weingarten surfaces in hyperbolic 3-space ⋮ Almost paracomplex structures on 4-manifolds ⋮ On the Gauss map of equivariant immersions in hyperbolic space ⋮ Geodesic paths of circles in the plane ⋮ Null hypersurfaces in 4-manifolds endowed with a product structure ⋮ A para-Kähler structure in the space of oriented geodesics in a real space form ⋮ On the geometry of spaces of oriented geodesics ⋮ Isometric immersions of the hyperbolic plane into the hyperbolic space ⋮ Marginally trapped surfaces in spaces of oriented geodesics ⋮ Global smooth geodesic foliations of the hyperbolic space ⋮ Spaces of geodesics of pseudo-Riemannian space forms and normal congruences of hypersurfaces ⋮ On the space of oriented geodesics of hyperbolic 3-space ⋮ On minimal Lagrangian surfaces in the product of Riemannian two manifolds ⋮ On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms

Cites Work

• Monopoles and geodesics
• Line congruences as surfaces in the space of lines
• On the space of oriented affine lines in \(\mathbb{R}^3\)
• On the geometry of the space of oriented lines of Euclidean space
• An Indefinite Kähler Metric on the Space of Oriented Lines
• The geometry of homogeneous submanifolds of hyperbolic space

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