Nonorientable minimal surfaces.

Meeks' minimal Moebius strip
Meeks' minimal Möbius strip. One end and total curvature -6p. López minimal Klein bottle. One end and total curvature -8p. A highly symmetrical minimal surface (López and Martín). This surface belongs to a family of nonorientable minimal surfaces with a dihedral group of symmetries of large order. This example is the topological sum of three Möbius strips, the symmetry group is isomorphic to D(3) and the total curvature is -14 p.
Both examples have critical total curvature, i.e. they minimize the total curvature among the surfaces with their respective (nonorientable) topology.


 Mathematica 2.2 for Solaris.


Copyright: Francisco Martin.