Calculating gaussian curvature

Asked Sep 01 '19 at 20:02

Active Sep 01 '19 at 21:14

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I am stuck with this problem. The quadric surface $xy=z^2+z$ is given to me, and I have to find the gaussian curvature in $(0,0,0)$. Is there an easy way? I have tried parametrizing it but I was unable to do that.

Can I go to the projective space, and choose $z+w=0$ as the plan at infinity? Doing that I can find an easy parametrization, but I am not sure the gaussian curvature remains the same.

Thanks

edited Sep 01 '19 at 21:14

KReiser

65,137

asked Sep 01 '19 at 20:02

Extreme_Math

Have you considered the formulas given here? – Intelligenti pauca Sep 01 '19 at 20:19
Can you solve (say, using implicit differentiation) for the second-order partial derivatives of $z=f(x,y)$ at the origin? (Or, even easier, in this case you could find $f(x,y)$ explicitly, just using the quadratic formula.) – Ted Shifrin Sep 01 '19 at 21:56

Calculating gaussian curvature

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