Georgiou, Nikos On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space. (English) Zbl 1272.53048 Math. Scand. 111, No. 2, 187-209 (2012). 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. Reviewer: Huili Liu (Shenyang) Cited in 1 ReviewCited in 3 Documents MSC: 53C40 Global submanifolds 53A25 Differential line geometry 53A35 Non-Euclidean differential geometry 53C30 Differential geometry of homogeneous manifolds Keywords:area stationary surface; holomorphic curve; Lagrangian surface PDFBibTeX XMLCite \textit{N. Georgiou}, Math. Scand. 111, No. 2, 187--209 (2012; Zbl 1272.53048) Full Text: DOI arXiv