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Bour surface companions in space forms. (English) Zbl 1346.53056

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 17th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 5–10, 2015. Sofia: Avangard Prima. 256-269 (2016).
Summary: In this paper, we give explicit parametrizations for Bour type surfaces in various three-dimensional space forms, using Weierstrass-type representations. We also determine classes and degrees of some Bour type zero mean curvature surfaces in three-dimensional Minkowski space.
For the entire collection see [Zbl 1330.53003].

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A35 Non-Euclidean differential geometry
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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Full Text: Euclid