TOPICS
Search

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

Phi_N(x_1,x_2,...,x_N)=sum_(d=1)^N(-1)^dsum_(i+j+...+m=N)x_ix_j...x_m_()_(d)=0.
(2)

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 Cubic

Explore with Wolfram|Alpha

References

Eastwood, M. and Ezhov, V. "Cayley Hypersurfaces." 25 Jan 2000. http://arxiv.org/abs/math.DG/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 Surface

Cite this as:

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

Subject classifications