Unduloids and their geometry. (English) Zbl 1199.53008

Hadzhilazova, Mariana; Mladenov, Ivaïlo M.; Oprea, John

Arch. Math., Brno 43, No. 5, 417-429 (2007).

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

Keywords:

mean curvature; unduloid