Veronese Surface
A smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations
| v(x,y,z)=(x^2,y^2,z^2,xy,xz,yz). |
The surface can be projected smoothly into four-space, but all three-dimensional projections have singularities (Coffman). The projections of these surfaces in three dimensions are called Steiner surfaces. The volume of the Veronese surface is 2pi^2.
See also
Steiner SurfaceExplore with Wolfram|Alpha
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References
Coffman, A. "Steiner Surfaces." http://www.ipfw.edu/math/Coffman/steinersurface.html.Referenced on Wolfram|Alpha
Veronese SurfaceCite this as:
Weisstein, Eric W. "Veronese Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VeroneseSurface.html