## Tohoku Mathematical Journal

### Isometric immersions of the hyperbolic plane into the hyperbolic space

Atsufumi Honda

#### 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

#### 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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