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Zbl 1051.53005
Mladenov, Iva\" ilo; Oprea, John
Unduloids and their closed geodesics. (English)
[A] Mladenov, Iva\"ilo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6--15, 2002. Sofia: Coral Press Scientific Publishing. 206-234 (2003). ISBN 954-90618-4-1/pbk

The authors give parametrizations for the unduloids in terms of Jacobi elliptic functions and use Clairaut's theorem to obtain explicit (in terms of an integral) parametrizations for geodesics on unduloids. Numerical integration and an intermediate value argument is then used to determine closed geodesics. The authors provide Maple code and surface graphics to illustrate their work.
[Udo Hertrich-Jeromin (Bath)]

MSC 2000:: *53A10 Minimal surfaces, surfaces with prescribed mean curvature
53C22 Geodesics

Keywords: closed geodesic; Delaunay surface; unduloid; Jacobi elliptic function; Clairaut's theorem

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