Re: a 4d algebraic geometry problem

• To: mathgroup at smc.vnet.net
• Subject: [mg110779] Re: a 4d algebraic geometry problem
• From: Roger Bagula <roger.bagula at gmail.com>
• Date: Mon, 5 Jul 2010 21:15:08 -0400 (EDT)
• References: <i0sal3\$epu\$1@smc.vnet.net>

```I used a minimal surface embedding of a sphere to get this
visualization:
x = Cos[t0]*Sin[p0]; y = Sin[t0]*Sin[p0]; z = Cos[p0];
x1 = Re[Integrate[x^2 + (22/16)*x*t + 1/3, {p0, 0, t}]];
y1 = Re[Integrate[y^2 + (22/16)*y*t + 1/3, {p0, 0, t}]];
z1 = Re[Integrate[z^2 + (22/16)*z*t + 1/3, {p0, 0, t}]];
g1 = ParametricPlot3D[{x1, y1, z1}, {t, 0, 2*Pi}, {t0, 0, 2*Pi}]
g2 = ParametricPlot3D[{x1, y1, z1}, {t, -2*Pi, 0}, {t0, 0, 2*Pi}]
g3 = ParametricPlot3D[{x1, y1, -z1}, {t, 0, 2*Pi}, {t0, -2*Pi, 0}]
g4 = ParametricPlot3D[{x1, y1, -z1}, {t, -2*Pi, 0}, {t0, -2*Pi, 0}]
Show[{g1, g2}, Boxed -> False, Axes -> False]
Show[{g3, g4}, Boxed -> False, Axes -> False]

Kind of a cludge,
but better than nothing.
Roger Bagula

```

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