Wente torus

In differential geometry, a Wente torus is an immersed torus in ${\displaystyle \mathbb {R} ^{3}}$ of constant mean curvature, discovered by Henry C. Wente (1986). It is a counterexample to the conjecture of Heinz Hopf that every closed, compact, constant-mean-curvature surface is a sphere (though this is true if the surface is embedded). There are similar examples known for every positive genus.

References

• Wente, Henry C. (1986), "Counterexample to a conjecture of H. Hopf.", Pacific Journal of Mathematics, 121: 193–243, doi:10.2140/pjm.1986.121.193, MR 0815044
• The Wente torus, University of Toledo Mathematics Department, retrieved 2013-09-01.

External links

• Visualization of the Wente torus