I have this expression:

$\int g^{m \bar{n}} g^{r\bar{p}} \partial_t {g}_{m r} \partial_t {g}_{\bar{n}\bar{p}} ~ d^6 y = f(t)$

Where m,n,p,r=1,2,3 and the $\bar{}$ are just the complex coordinates.

Any idea guys how to plot the left hand side of g with the knowledge of f(t) ?

$g^{m\bar{n}}$ is a 3x3 complex matrix.

It’s like $g_{\mu\nu}$ in the Riemannien line element $ ds^2 =g_{\mu\nu} dx^\mu dx^\nu$ , but we know the elements of $g_{\mu\nu}$, while $g_{mr}$ only what I know about is the above relation to some function f(t). I can plot this in 3D or ContourPlot, …

Maybe I search for a final result like in answer 1 in the following question:

How would I plot the metric $ds^2 =−(\phi^2 t^2)dt^2+dx^2+dy^2$ in Mathematica?

Any help appreciated!


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