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A developable surface in
hyperbolic space is a ruled surface (the trace of a moving hyperbolic line) whose
tangent hyperbolic plane is constant along elements. This paper discusses the
following hyperbolic analogs of theorems on developable surfaces in euclidean
space:
1. A ruled surface is developable if and only if the tangent to the directrix, the
unit vector giving the direction of the element, and the covariant derivative of the
latter along the directrix, are linearly dependent.
2. A developable surface consists of portions of cones, tangential surfaces, and
geodesic cylinders (to be defined).
3. A developable surface is applicable on a hyperbolic plane.
4. A flat surface in hyperbolic space (a surface whose intrinsic curvature is the same
as that of a hyperbolic plane) is necessarily developable.
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