Flat surfaces in hyperbolic space as normal surfaces to a congruence of geodesics

DOI10.2748/tmj/1176734745zbMath1140.53004OpenAlexW2007989665MaRDI QIDQ2471135

Pedro Roitman

Publication date: 22 February 2008

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1176734745

zbMATH Keywords

flat surfacescausticsWeierstrass representation

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Rigidity results (53C24)

Related Items (18)

Asymptotic behavior of flat surfaces in hyperbolic 3-space ⋮ Legendrian dual surfaces in hyperbolic 3-space ⋮ Isometric immersions of \(\mathbb L^2\) into \(\mathbb L^4\) ⋮ Isometric immersions with singularities between space forms of the same positive curvature ⋮ A characterization of Weingarten surfaces in hyperbolic 3-space ⋮ Focal surfaces of fronts associated to unbounded principal curvatures ⋮ DERIVED SCHWARZ MAP OF THE HYPERGEOMETRIC DIFFERENTIAL EQUATION AND A PARALLEL FAMILY OF FLAT FRONTS ⋮ Value distribution of the Gauss map of improper affine spheres ⋮ A connection between flat fronts in hyperbolic space and minimal surfaces in Euclidean space ⋮ Complete flat surfaces with two isolated singularities in hyperbolic 3-space ⋮ On the generalized Weyl problem for flat metrics in the hyperbolic 3-space ⋮ Ribaucour transformations for flat surfaces in the hyperbolic 3-space ⋮ Extrinsic diameter of immersed flat tori in \(S^3\) ⋮ On the space of oriented geodesics of hyperbolic 3-space ⋮ Hypersurfaces in hyperbolic space associated with the conformal scalar curvature equation \(\Delta u +ku^{\frac{n+2}{n-2}}=0\) ⋮ Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space ⋮ Embedded isolated singularities of flat surfaces in hyperbolic 3-space ⋮ Schwarz maps for the hypergeometric differential equation

Cites Work

• An elementary proof of Small's formula for null curves in \(\text{PSL}(2,\mathbb{C})\) and a analogue for Legendrian curves in \(\text{PSL}(2,\mathbb{C})\)
• Flat fronts in hyperbolic 3-space
• Flat surfaces in the hyperbolic 3-space
• Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method
• On complete flat surfaces in hyperbolic $3$-space
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Flat surfaces in hyperbolic space as normal surfaces to a congruence of geodesics