Wente torus

In differential geometry, a Wente torus is an immersed torus in $\mathbb {R} ^{3}$ 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 0815044193-243&rft.date=1986&rft_id=info:doi/10.2140/pjm.1986.121.193&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=0815044#id-name=MR&rft.aulast=Wente&rft.aufirst=Henry C.&rft_id=http://projecteuclid.org/euclid.pjm/1102702809&rfr_id=info:sid/en.wikipedia.org:Wente torus" class="Z3988">
The Wente torus, University of Toledo Mathematics Department, retrieved 2013-09-01.