Karcher JD Saddle Tower
Karcher JD Saddle Tower is a doubly periodic minimal surface, given by a Weierstrass representation, immersed, with a layer group.
Open Karcher JD Saddle Tower in the interactive viewer →
def-weierstrass doubly-periodic immersed implemented minimal minimal-periodic tradition-classical
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- doubly periodic
- Ends
- 0
- Embedding
- immersed
- Symmetry kind
- layer group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Doubly periodic embedded conjugate pair of minimal surfaces suggested by the Scherk saddle towers; unlike the JE family the towers are separated by a planar symmetry line, and by a rare coincidence the conjugate family consists of the same surfaces with the parameter running backwards. Morphing parameter: edge length ratio of the rectangular torus domain.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- H. Karcher, "Construction of minimal surfaces", in "Surveys in Geometry", Univ. of Tokyo, 1989, and Lecture Notes No. 12, SFB 256,
- H. Karcher, "Embedded minimal surfaces derived from Scherk's examples", Manuscripta Math. 62 (1988) 83-114 -- the JD/JE tower families.
- The 3DXM Consortium, "Wavy Enneper", "Karcher JD Saddle Tower" and "Karcher JE Saddle Tower" exhibits, https://virtualmathmuseum.org/
- Bonn, 1989, pp. 1-96 -- the Enneper-end language and the doubly periodic examples (section 3.3).
- - the exact exhibit data (Gauss map, dh, parameter ranges) followed here.
- A. Enneper (1864) -- the base surface the waves ride on.
- The 3DXM Consortium, 'Karcher JD Saddle tower', Virtual Math Museum, virtualmathmuseum.org (local mirror: vmm/book/surface/ch027_karcher_jd_st.md).
- H. Karcher, 'Embedded minimal surfaces derived from Scherk's examples', Manuscripta Math. 62 (1988) 83-114.