Isometric Immersions of the Hyperbolic Plane into the Hyperbolic Space

2010/09/21 by Atsufumi Honda, Honda, Atsufumi
Mathematics · #53A35 #53C22 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A35 #msc:53C22 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1009.3994

20 pages, 5 figures

arxiv created 2010/09/21 · arxiv updated 2010/09/22

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.

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