Wente Torus
Wente Torus is a constant-mean-curvature surface, given by a parametrisation, genus 1, immersed.
Open Wente Torus in the interactive viewer →
aperiodic closed closed-orientable cmc def-parametric immersed implemented tradition-classical
Properties
- Family
- cmc
- Given by
- a parametrisation
- Curvature
- constant mean curvature
- Periodicity
- not periodic
- Genus
- 1
- Ends
- 0
- Embedding
- immersed
- Orientable
- yes
- Fidelity
- exact
Definition
No chart is stored: the immersion needs theta functions on the twisted torus; the builder evaluates it numerically and no elementary closed form exists. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- H. C. Wente, 'Counterexample to a conjecture of H. Hopf', Pacific J. Math. 121 (1986).
- R. Walter, 'Explicit examples to the H-problem of Heinz Hopf', Geom. Dedicata 23 (1987) -- the elementary parametrisation used here (supplement 6.B').