I think that the general way of asking the question is the following: how can I ask Mathematica to plot a function on a certain plane?

A simple example.

Let's assume a function that is given by $$\begin{align} \begin{aligned} X &= X_0+X_1+X_2 \\ X_0 &= 3 \tau \\ X_1 &= \cos(3 \tau) \cos(3 \sigma)\\ X_2 &= \sin(3 \tau) \cos(3 \sigma) \end{aligned} \end{align}$$

How can I plot the function X in the $(X_1,X_2)$-plane?

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    $\begingroup$ The definition of X is unclear, seems to be a scalar.. Is a spacepoint defined as {X0,X1,X2} ? $\endgroup$ Jan 27 '20 at 11:49
  • $\begingroup$ @UlrichNeumann It is a scalar. And the space point is defined as having the coordinates you mentioned. The coordinates σ and τ are the result of the spacetime embedding. $\endgroup$ Jan 27 '20 at 12:00
  • $\begingroup$ x0=3 tau=constdefine the planes you're looking for. Eliminating sigma, tau gives ( X1/Cos[x0)^2+( X2/Sin[x0)^2==1 (ellipse). $\endgroup$ Jan 27 '20 at 12:19

Knowing the elliptic constraint ( X1/Cos[x0)^2+( X2/Sin[x0)^2==1 (see my comment) the parametric form of the planes x0==const is

x1=Cos[x0] Cos[t];
x2=Sin[x0] Sin[t];
p[t_, x0_] := Evaluate[ {x1, x2, x0 + x1 + x2}  ]

ParametricPlot3D gives the plot

ParametricPlot3D[p[t, 0.5], {t, 0, 2 Pi},AxesLabel -> {"x1", "x2", "x"}]

enter image description here

you're looking for!

  • $\begingroup$ thanks for your comment and the answer. $\endgroup$ Jan 27 '20 at 14:33
  • $\begingroup$ You're welcome! $\endgroup$ Jan 27 '20 at 14:45

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