Rattlesnake Tori

Constant mean curvature tori in euclidean 3-space

Two examples of spectral-genus-three tori, constructed by bending a straight spectral-genus-two cylinder [2].

A straight cylinder of spectral genus 2, to be bent into a rattlesnake torus of spectral genus 3.
Rattlesnake torus.
A straight cylinder of spectral genus 2, to be bent into a rattlesnake torus of spectral genus 3.
Rattlesnake torus.

References

  1. John Bolton, Franz Pedit and Lyndon Woodward, Minimal surfaces and the affine Toda field model, J. Reine Angew. Math. 459 (1995), 119–150.
  2. N. J. Hitchin, Harmonic maps from a 2-torus to the 3-sphere, J. Differential Geom. 31 (1990), no. 3, 627–710.
  3. M. Kilian and M. U Schmidt, On the moduli of constant mean curvature cylinders of finite type in the 3-sphere, arXiv:0712:0108v2, 2008.
  4. N. Schmitt, Flowing CMC cylinders to tori, Preprint, 2008.