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Planar p-elasticae and rotational linear Weingarten surfaces. (English) Zbl 1415.53002

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 20th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 2–7, 2018. Sofia: Avangard Prima; Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 20, 227-238 (2019).
Summary: We variationally characterize the profile curves of rotational linear Weingarten surfaces as planar p-elastic curves. Moreover, by evolving these planar p-elasticae under the binormal flow with prescribed velocity, we describe a procedure to construct all rotational linear Weingarten surfaces, locally. Finally, we apply our findings to two well-known family of surfaces.
For the entire collection see [Zbl 1408.53003].

MSC:

53A04 Curves in Euclidean and related spaces
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
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