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Unduloids and their geometry. (English) Zbl 1199.53008
Summary: We consider non-compact cylinder-like surfaces called unduloids and study some aspects of their geometry. In particular, making use of a Kenmotsu-type representation of these surfaces, we derive explicit formulas for the lengths and areas of arbitrary segments, along with a formula for the volumes enclosed by them.

MSC:
53A05 Surfaces in Euclidean and related spaces
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53-04 Software, source code, etc. for problems pertaining to differential geometry
49Q10 Optimization of shapes other than minimal surfaces
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