Eguchi-Hanson Space
Eguchi-Hanson Space is a surface, given by a parametrisation, immersed.
Open Eguchi-Hanson Space in the interactive viewer →
aperiodic def-parametric immersed implemented misc
Properties
- Family
- misc
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: the bolt slice's height is obtained by integrating z'(r) with the trapezium rule over 160 steps (`eguchi_hanson_profile`); rho is closed form but z is a quadrature, so the revolved profile has no expression in the exact language. 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.
- D. von Seggern, "CRC Standard Curves and Surfaces" (1993), p. 304 -- Fresnel's elasticity surface.
- A. Robin (2004), plotted after M. Trott, "The Mathematica GuideBook for Graphics" (2004), p. 103 -- the paper bag surface.
- O. Knill (2017); M. A. Villarino and J. C. Varilly (2024) -- the trihyperboloid and its volume ln 256.
- C. Dupin, "Applications de Geometrie et de Mechanique", Paris 1822;
- B. Odehnal, "Ortho-Circles of Dupin Cyclides", J. Geometry Graphics 10 (2006) 1-21 -- the inversion construction and the ring / horn / spindle classification.
- J. Tannery, Bulletin des sciences mathematiques, 2e serie, 16 (1892) 190; O. Zoll, "Ueber Flaechen mit Scharen geschlossener geodaetischer Linien", Math. Ann. 57 (1903) 108-133; A. L. Besse, "Manifolds all of whose Geodesics are Closed", Springer 1978.