Beyond Delaunay surfaces. (English) Zbl 1203.53007

Djondjorov, Peter A.; Hadzhilazova, Mariana Ts.; Mladenov, Ivaïlo M.; Vassilev, Vassil M.

J. Geom. Symmetry Phys. 18, 1-11 (2010).

Summary: An interesting class of axially symmetric surfaces, which generalizes Delaunay’s unduloids and provides solutions of the shape equation is described in explicit parametric form. This class provide the first analytical examples of surfaces with periodic curvatures studied by K. Kenmotsu and leads to some unexpected relationships among Jacobian elliptic functions and their integrals.

MSC:

53A10

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

Jacobian elliptic functions; vesicle; shape energy; spontaneous curvature; bending; Gaussian rigidity