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Gaussian curvature

Julio

Member
Feb 14, 2014
71
Show that if $S=(x,y,h(x,y)): (x,y)\in U$ where $h: U\to \mathbb{R}$ is a smooth function then $K=\dfrac{\text{det}\, \text{Hess}\, h}{(1+\left| \nabla h \right|^2)^2}.$

Hello, we can use that $K=\dfrac{eg-f^2}{EG-F^2}$. Yes?
 

Euge

MHB Global Moderator
Staff member
Jun 20, 2014
1,890
Hi Julio ,

Yes, you can (and, in fact, should) use that formula to compute that Gaussian curvature.