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On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space. (English) Zbl 1272.53048

The author proves that there are no holomorphic curves of rank 1 and that a surface which is Lagrangian of rank 1 can not be area stationary. Then the author proves that every holomorphic curve is area stationary. He classifies all Lagrangian area stationary surfaces and obtains a two parameter family of area stationary rotationally symmetric surfaces that are neither Lagrangian nor holomorphic.

MSC:

53C40 Global submanifolds
53A25 Differential line geometry
53A35 Non-Euclidean differential geometry
53C30 Differential geometry of homogeneous manifolds
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