0
$\begingroup$

I see many methods to calculate the Gaussian curvature of parametric surfaces in SE.But how to calculate the Gaussian curvature of any point of the following explicit function:

f[x_, y_] := x^2 + y^2
$\endgroup$
2
  • 2
    $\begingroup$ You can easily use a Gaussian curvature routine intended for parametric surfaces on a Monge patch. Using e.g. GaussianCurvature[] from here, try this: GaussianCurvature[{x, y, x^2 + y^2}, {x, y}] $\endgroup$ Jan 29 '20 at 8:44
  • $\begingroup$ @J. M. But how to eliminate the singularity of the curvature of this function:gccolor[{x, y, (x^4 - 6 x^2 y^2 + y^4)/(x^2 + y^2)^2 BesselJ[4, 17 Sqrt[x^2 + y^2]]} /. {x -> u, y -> v}, {u, -1, 1 }, {v, -1, 1}] $\endgroup$ Jan 29 '20 at 9:23