Isometric immersions of the hyperbolic plane into the hyperbolic space
Copyright policy )Isometric immersions of the hyperbolic plane into the hyperbolic space
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.
20 pages, 5 figures
Mathematics - Differential Geometry, Kähler and para-Kähler structure, neutral metric, 53C50, Global submanifolds, null curve, Geodesics in global differential geometry, 53A35, 53C22, Hyperbolic space, null-causal curve, developable surface, ideal cone, hyperbolic space, minitwistor space, Differential Geometry (math.DG), FOS: Mathematics, Non-Euclidean differential geometry, 53A35, 53C22, 53C50
Mathematics - Differential Geometry, Kähler and para-Kähler structure, neutral metric, 53C50, Global submanifolds, null curve, Geodesics in global differential geometry, 53A35, 53C22, Hyperbolic space, null-causal curve, developable surface, ideal cone, hyperbolic space, minitwistor space, Differential Geometry (math.DG), FOS: Mathematics, Non-Euclidean differential geometry, 53A35, 53C22, 53C50
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