Kokubu, Masatoshi Weierstrass representation for minimal surfaces in hyperbolic space. (English) Zbl 0912.53041 Tôhoku Math. J., II. Ser. 49, No. 3, 367-377 (1997). The author intends to give a Weierstrass kind formula for minimal surfaces in hyperbolic space. He defines a notion of Gauss map and proves some statements. Reviewer: Ricardo Sa Earp (Rio de Janeiro) Cited in 2 ReviewsCited in 22 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:Weierstrass representation; minimal surfaces; hyperbolic space PDFBibTeX XMLCite \textit{M. Kokubu}, Tôhoku Math. J. (2) 49, No. 3, 367--377 (1997; Zbl 0912.53041) Full Text: DOI References: [1] R. BRYANT, Surfaces of mean curvature one in hyperbolic space, Asterisque 154-155 (1987), 321-347. · Zbl 0635.53047 [2] M. DO CARMO AND M. DAJCZER, Rotational hypersurfaces in spaces of constant curvature, Trans Amer. Math. Soc. 277 (1983), 685-709. · Zbl 0518.53059 · doi:10.2307/1999231 [3] CH. L. EPSTEIN, The hyperbolic Gauss map and quasiconformal reflections, J. Reine Angew Math. 372 (1986), 96-135. · Zbl 0591.30018 · doi:10.1515/crll.1986.372.96 [4] R. D. GULLIVER, II, R. OSSERMAN AND H. L. ROYDON, A theory of branched immersions o surfaces, Amer. J. Math. 95 (1973), 750-812. JSTOR: · Zbl 0295.53002 · doi:10.2307/2373697 [5] K. KENMOTSU, Weierstrass formula for surfaces of prescribed mean curvature, Math. Ann. 24 (1979), 89-99. · Zbl 0402.53002 · doi:10.1007/BF01428799 [6] M. OBATA, The Gauss map of immersions of Riemannian manifoldsin space of constant curvature, J. Differential Geom. 2 (1968), 217-223. · Zbl 0181.49801 [7] K. UHLENBECK, Harmonic maps into Lie groups (classical solutions of the chiral model), J. Differential Geom. 30 (1989), 1-50. · Zbl 0677.58020 [8] M. UMEHARA AND K. YAMADA, Complete surfaces of constant mean curvature one in th hyperbolic 3-space, Ann.of Math, 137 (1993), 611-638. JSTOR: · Zbl 0795.53006 · doi:10.2307/2946533 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.