Wente Torus

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In 1894, Henry Wente discovered the Wente torus, an immersed torus of constant (but not zero) mean curvature. Such constant mean curvature (CMC) surfaces are counterexamples to Hopf's conjecture that a sphere is the only closed surface with constant mean curvature that is compact [1]. The set of all symmetric tori is in one-to-one correspondence with the set of reduced fractions ; each corresponds to a symmetric Wente torus labeled as [2].

Contributed by: Enrique Zeleny (June 2014)
Open content licensed under CC BY-NC-SA




[1] H. C. Wente, "Counterexample to a Conjecture of H. Hopf," Pacific Journal of Mathematics, 121(1), 1986 pp. 193–243. projecteuclid.org/euclid.pjm/1102702809.

[2] Marija Ćirić, "Notes on Constant Mean Curvature Surfaces and Their Graphical Presentation," Filomat 23(2), 2009 pp. 97–107. www.pmf.ni.ac.rs/pmf/publikacije/filomat/2009/23-2-2009/Paper10.pdf.

[3] M. Heil. CMC: Pictures of Constant Mean Curvature Tori [Video]. (Jun 16, 2014) www.youtube.com/watch?v=7rnsdcS7qGU.

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