Tohoku Mathematical Journal

Isometric immersions of the hyperbolic plane into the hyperbolic space

Atsufumi Honda

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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

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

First available in Project Euclid: 2 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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