Tohoku Mathematical Journal
2012
June
SECOND SERIES VOL. 64, NO. 2

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

Title ISOMETRIC IMMERSIONS OF THE HYPERBOLIC PLANE INTO THE HYPERBOLIC SPACE

Author Atsufumi Honda

(Received September 22, 2010, revised April 26, 2011)
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.

2000 Mathematics Subject Classification. Primary 53A35; Secondary 53C22, 53C50.
Key words and phrases. Hyperbolic space, developable surface, null curve, Kähler and para-Kähler structure, minitwistor space.

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