Kourouniotis, Christos Bending in the space of quasi-Fuchsian structures. (English) Zbl 0718.57010 Glasg. Math. J. 33, No. 1, 41-49 (1991). The author presents a generalization of the idea of bending a hyperbolic n-manifold M along an embedded totally geodesic hypersurface [see W. Thurston, The geometry and topology of 3-manifolds, Princeton Duplicated Notes, 1978-1979; B. Apanasov, Proc. 1978 Stony Brook Conf., Ann. Math. Stud. 97, 21-31 (1981; Zbl 0464.30037); the author, Math. Proc. Camb. Philos. Soc. 98, 247-261 (1985; Zbl 0577.53041)]. This generalization is possible only for the case \(n=2\) (i.e. M is a surface) and deals with a deformation of M along any geodesic lamination on the surface M. In the case of a lamination, the author does not obtain an explicit bending embedding of the hyperbolic plane \({\mathbb{H}}^ 2\) (universal covering of M) into \({\mathbb{H}}^ 3\) but defines a deformation of M by an approximation construction of its infinitesimal deformation, i.e. its cocycles. Reviewer: B.N.Apanasov (Norman) Cited in 4 Documents MSC: 57R40 Embeddings in differential topology 30F45 Conformal metrics (hyperbolic, Poincaré, distance functions) Keywords:hyperbolic manifold; bending; totally geodesic hypersurface; deformation; geodesic lamination Citations:Zbl 0464.30037; Zbl 0577.53041 PDFBibTeX XMLCite \textit{C. Kourouniotis}, Glasg. Math. J. 33, No. 1, 41--49 (1991; Zbl 0718.57010) Full Text: DOI References: [1] Kourouniotis, Bending punctured tori. [2] Epstein, Analytical and geometric aspects of hyperbolic space 111 pp 113– (1987) [3] Thurston, The geometry and topology of 3-manifolds (1978) [4] DOI: 10.1017/S030500410006343X · Zbl 0577.53041 · doi:10.1017/S030500410006343X 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.