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Characterizations of Bianchi-Bäcklund transformations of constant mean curvature surfaces. (English) Zbl 1083.53011

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)].

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53A05 Surfaces in Euclidean and related spaces

Citations:

Zbl 0892.53003
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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
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