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Nepali Surface

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nepali surface with its singular curve and isolated singular point marked in orange

The Nepali surface is the sextic surface

(xy-z^3-1)^2=(1-x^2-y^2)^3,

named by Hauser (Real Sociedad Matemática Española 2011, p. 27). It is bounded. For every real point on the surface, the nonnegative left side forces x^2+y^2<=1. The equation then also bounds z, since |z^3|<=|xy|+1+(1-x^2-y^2)^(3/2)<=5/2.

The real singular points consist of the origin and the closed curve x^2+y^2=1, z^3=xy-1.

See also

Sextic Surface

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References

Hauser, H. "Gallery of Singular Algebraic Surfaces: Nepali." https://homepage.univie.ac.at/herwig.hauser/gallery.html.Real Sociedad Matemática Española. RSME-IMAGINARY: Una mirada matemática. Madrid, Spain: Real Sociedad Matemática Española, p. 27, 2011. https://fme.upc.edu/ca/exposicio-imaginary-una-simfonia-matematica-fme-2021/material-docemt/rsmeimaginary_catalogue_es.pdf.

Cite this as:

Weisstein, Eric W. "Nepali Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NepaliSurface.html

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