Bulletin of the Belgian Mathematical Society - Simon Stevin

Parabolic surfaces in hyperbolic space with constant Gaussian curvature

Rafael López

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Abstract

A parabolic surface in hyperbolic space $\mathbb H^3$ is a surface invariant by a group of parabolic isometries. In this paper we describe all parabolic surfaces with constant Gaussian curvature. We study the qualitative properties such as completeness and embeddedness.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 2 (2009), 337-349.

Dates
First available in Project Euclid: 3 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1244038144

Digital Object Identifier
doi:10.36045/bbms/1244038144

Mathematical Reviews number (MathSciNet)
MR2541046

Zentralblatt MATH identifier
1173.53026

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)

Keywords
hyperbolic space parabolic surface Gaussian curvature

Citation

López, Rafael. Parabolic surfaces in hyperbolic space with constant Gaussian curvature. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 2, 337--349. doi:10.36045/bbms/1244038144. https://projecteuclid.org/euclid.bbms/1244038144


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