Kobayashi, Shimpei; Inoguchi, Jun-ichi Characterizations of Bianchi-Bäcklund transformations of constant mean curvature surfaces. (English) Zbl 1083.53011 Int. J. Math. 16, No. 2, 101-110 (2005). After a brief but lucid introduction into the transformation theory of surfaces the authors show that Bianchi-Bäcklund transformations of constant mean curvature surfaces are equivalent to Darboux transformations and simple type dressings. In particular this disproves a conjecture of U. Hertrich-Jeromin and F. Pedit in [Doc. Math., J. DMV 2, 313–333 (1997; Zbl 0892.53003)]. Reviewer: Dirk Ferus (Berlin) Cited in 8 Documents MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A05 Surfaces in Euclidean and related spaces Keywords:Darboux transformations Citations:Zbl 0892.53003 PDFBibTeX XMLCite \textit{S. Kobayashi} and \textit{J.-i. Inoguchi}, Int. J. Math. 16, No. 2, 101--110 (2005; Zbl 1083.53011) Full Text: DOI References: [1] Bianchi L., Vorlesungen über Differentialgeometrie (1910) · JFM 41.0676.01 [2] Hertrich-Jeromin U., Doc. Math. 2 pp 313– [3] Kobayashi S.-P., Balkan J. Geom. Appl. 9 pp 46– [4] DOI: 10.1512/iumj.1993.42.42057 · Zbl 0803.53009 · doi:10.1512/iumj.1993.42.42057 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.