Tohoku Mathematical Journal

Isometric immersions of the hyperbolic plane into the hyperbolic space

Atsufumi Honda

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Abstract

In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we characterize “ideal cones” (i.e., cones whose vertices are on the ideal boundary) by behavior of their mean curvature.

Article information

Source
Tohoku Math. J. (2), Volume 64, Number 2 (2012), 171-193.

Dates
First available in Project Euclid: 2 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1341249370

Digital Object Identifier
doi:10.2748/tmj/1341249370

Mathematical Reviews number (MathSciNet)
MR2948818

Zentralblatt MATH identifier
1252.53015

Subjects
Primary: 53A35: Non-Euclidean differential geometry
Secondary: 53C22: Geodesics [See also 58E10] 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Hyperbolic space developable surface null curve Kähler and para-Kähler structure minitwistor space

Citation

Honda, Atsufumi. Isometric immersions of the hyperbolic plane into the hyperbolic space. Tohoku Math. J. (2) 64 (2012), no. 2, 171--193. doi:10.2748/tmj/1341249370. https://projecteuclid.org/euclid.tmj/1341249370


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