Cayley Surface
In affine three-space the Cayley surface is given by
| x_3=x_1x_2-1/3x_1^3 |
(1)
|
(Nomizu and Sasaki 1994). The surface has been generalized by Eastwood and Ezhov (2000) to
This gives the first few hypersurfaces as
x_4 = x_1x_3+1/2x_2^2-x_1^2x_2+1/4x_1^4
(3)
x_5 = x_1x_4+x_2x_3-x_1^2x_3-x_1x_2^2+x_1^3x_2-1/5x_1^5.
(4)
See also
Cayley CubicExplore with Wolfram|Alpha
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References
Eastwood, M. and Ezhov, V. "Cayley Hypersurfaces." 25 Jan 2000. https://arxiv.org/abs/math/0001134.Nomizu, K. and Pinkall, U. "Cayley Surfaces in Affine Differential Geometry." Tôhoku Math. J. 41, 589-596, 1989.Nomizu, K. and Sasaki, T. Affine Differential Geometry: Geometry of Affine Immersions. Cambridge, England: Cambridge University Press, 1994.Referenced on Wolfram|Alpha
Cayley SurfaceCite this as:
Weisstein, Eric W. "Cayley Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CayleySurface.html